![Ordinarily, this might have won him votes in tolerant south
Louisiana, where prohibition was regarded as the figment of sick
imaginations, like the loup garou. But in south Louisiana he had few
backers in that campaign to begin with, being a north Louisiana
hillman; and in north Louisiana, where drinking had to be done in
secret even before the Volstead Act became nominally the law of the
land, such reports were sheer poison.
Finally, the weather on election day turned foul. The wretched dirt
roads of the hinterlands where Huey’s voting strength was
concentrated became impassable, so that many of his supporters
could not reach their polling places. But four years later, when he
once more ran for governor in yet another three-man race, he barely
missed a majority in the first primary. No run-off was held, however,
because one of his opponents announced he would throw his
support to Long, pulling with him many followers, including a young
St. Landry parish physician, Dr. F. Octave Pavy, who had run for
lieutenant governor. Under the circumstances a second primary
would have been merely an empty gesture of defiance.
As governor, he rode roughshod over all opposition to his proposal
to furnish free textbooks to every school child, not merely in the
public schools, but in the Catholic parochial schools and the posh
private academies as well; for a highway-improvement program
which he proposed to finance out of increased gasoline taxes. Nor
was he one to hide his light under a bushel in pretended modesty.
On the contrary, after each success he rang the changes on Jack
Horner’s classic “What a good [in the sense of great] boy am I.”
Moreover, it made little difference to his devotees whether his
promises of still greater benefits for the future, or boasts about the
wonders he had already achieved, were based on fact or fiction.
By way of illustration: Dr. Arthur Vidrine, a back-country physician,
was catapulted into the superintendency of the state’s huge Charity
Hospital at New Orleans, and later was additionally made dean of
the new state university College of Medicine Long decided to found.
Vidrine had won the new governor’s warm regard by captaining the
Long cause in Ville Platte, where he was a general practitioner.](https://image.slidesharecdn.com/92006-250414223314-4576cdd8/85/Stochastic-Processes-From-Applications-to-Theory-1st-Edition-Pierre-Del-Moral-33-320.jpg)
![whom all anti-Long factions would agree to support against any
nominee the Senator might hand-pick for endorsement.
However, with what still appears to be a positive genius for
fumbling, the anti-Long leadership guarded with such butter-
fingered zeal the secret of whether, where, or when they were to
meet that even before they assembled, Long aides had ample time
to install the microphone of a dictograph in the room where the anti-
Long General Staff was to confer. The device functioned very fuzzily.
Its recording (which it was hoped to duplicate and replay from sound
trucks throughout the ensuing campaign) was only spottily
intelligible. But a couple of court reporters had also been equipped
with earphones at a listening post, and their stenographic transcript,
though incomplete, afforded some excerpts which Senator Long
inflated into what he presented as a full-scale murder plot.
His fulmination was delivered before a crowded gallery, as usual.
This popularity annoyed many of his senior colleagues, none more
so than Vice-President Garner, whom John L. Lewis was soon to
stigmatize as “that labor-baiting, poker-playing, whiskey-drinking evil
old man.” More than once, as the galleries emptied with a rush the
moment Long finished, Mr. Garner would call to the departing
auditors, saying: “Yes, you can go now! The show’s over!”
In this instance, as on many previous occasions, there was no
advance hint of the fireworks to come. The fuse was a debate over
the Frazier-Lemke bill, and Senator Long contented himself at the
outset with charging that the administration was conducting
“government by blackmail.” In making this statement he was
referring to NIRA, which had succeeded NRA, the latter having been
declared unconstitutional some three months earlier. This had
nothing to do with the Frazier-Lemke bill, but it gave Mr. Long an
opportunity to charge that no contracts for PWA work were being
financed unless the contractor agreed to abide by all the provisions
of the NRA code which the Supreme Court had invalidated.
That led to the statement that “we in Louisiana have never stood
for [such] blackmail from anybody,” which in turn led to a section of
his arraignment the Congressional Record headed:](https://image.slidesharecdn.com/92006-250414223314-4576cdd8/85/Stochastic-Processes-From-Applications-to-Theory-1st-Edition-Pierre-Del-Moral-47-320.jpg)
![quoted next, reading from the transcript, as suggesting that “we
have Dear to make a trip around the state and then announce that
the people want him to run for Governor, and no one will know
about this arrangement here ... as you all know we must all keep all
of this a secret and not even tell our own families of what is done.”
Whereupon, according to the record, another voice proposed that
“we should make fellows like Farley and Roosevelt and the suffering
corporations ... cough up enough to get rid of that fellow.”
Commented Senator Long: “Yes, we should make the Standard Oil
Company and the ‘suffering corporations’ cough up enough ... says
Mr. Sandlin ... [but] I am going to teach my friends in the Senate
how to lick this kind of corruption. I am going to show them how to
lick it to a shirttail finish.... I am going to give you a lesson in
January to show you that the crookedness and rottenness and
corruption of this Government, however ably [sic!] financed and
however many big corporations join in it, will not get to first base.”
More of the same sort of dialogue was read from the transcript.
Congressman Sandlin assured the meeting that President Roosevelt
will “endorse our candidate.” Another of the conferees, one
O’Rourke, was described by Long as having refused to testify when
another witness at an inquiry into one of Huey Long’s earlier murder-
plot charges “swore that he had hired O’Rourke to commit murder in
Baton Rouge. I was the man he was to kill so there was not much
said about it except that he refused to testify on the ground that he
would incriminate himself, whereupon Roosevelt employed him. He
was qualified and he was appointed.”
The statement most frequently quoted in the weeks and months
that followed was that of an unidentified voice which the transcript
reported as saying: “I would draw in a lottery to go out and kill
Long. It would take only one man, one gun and one bullet.” And
some time thereafter, according to the transcript, another
unidentified voice declared that “I haven’t the slightest doubt but
that Roosevelt would pardon any one who killed Long.” Thereupon
someone asked: “But how could it be done?” and the reply was:
“The best way would be to just hang around Washington and kill him
right in the Senate.”](https://image.slidesharecdn.com/92006-250414223314-4576cdd8/85/Stochastic-Processes-From-Applications-to-Theory-1st-Edition-Pierre-Del-Moral-49-320.jpg)
Stochastic Processes From Applications to Theory 1st Edition Pierre Del Moral
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- 5. Stochastic Processes From Applications to Theory 1st Edition Pierre Del Moral Digital Instant Download Author(s): Pierre Del Moral, Spiridon Penev ISBN(s): 9781498701839, 1498701833 Edition: 1 File Details: PDF, 21.77 MB Year: 2016 Language: english
- 8. CHAPMAN&HA LL/CRC TextsinStatis ticalSc ienceSe ries SeriesEditors FrancescaD ominici, HarvardSc hoolofPublic H ealth,U SA JulianJ .F araway, UniversityofBath,U K Martin Tanner,N orthwesternU niversity,U SA JimZide k,U niversityofBr itishC olumbia,C anada Statistical Theory: A Concise Introduction F. Abramovich and Y. Ritov Practical Multivariate Analysis, Fifth Edition A. Afifi, S. May, and V.A. Clark Practical Statistics for Medical Research D.G. Altman Interpreting Data: A First Course in Statistics A.J.B. Anderson Introduction to Probability with R K. Baclawski Linear Algebra and Matrix Analysis for Statistics S. Banerjee and A. Roy Mathematical Statistics: Basic Ideas and Selected Topics, Volume I, Second Edition P. J. Bickel and K. A. Doksum Mathematical Statistics: Basic Ideas and Selected Topics, Volume II P. J. Bickel and K. A. Doksum Analysis of Categorical Data with R C. R. Bilder and T. M. Loughin Statistical Methods for SPC and TQM D. Bissell Introduction to Probability J. K. Blitzstein and J. Hwang Bayesian Methods for Data Analysis, Third Edition B.P. Carlin and T.A. Louis Second Edition R. Caulcutt The Analysis of Time Series: An Introduction, Sixth Edition C. Chatfield Introduction to Multivariate Analysis C. Chatfield and A.J. Collins Problem Solving: A Statistician’s Guide, Second Edition C. Chatfield Statistics for Technology: A Course in Applied Statistics,Third Edition C. Chatfield Analysis of Variance, Design, and Regression : Linear Modeling for Unbalanced Data, Second Edition R. Christensen Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians R. Christensen, W. Johnson, A. Branscum, and T.E. Hanson Modelling Binary Data, Second Edition D. Collett Modelling Survival Data in Medical Research, Third Edition D. Collett Introduction to Statistical Methods for Clinical Trials T.D. Cook and D.L. DeMets Applied Statistics: Principles and Examples D.R. Cox and E.J. Snell Multivariate Survival Analysis and Competing Risks M. Crowder Statistical Analysis of Reliability Data M.J. Crowder, A.C. Kimber, T.J. Sweeting, and R.L. Smith An Introduction to Generalized Linear Models,Third Edition A.J. Dobson and A.G. Barnett Nonlinear Time Series:Theory, Methods, and Applications with R Examples R. Douc, E. Moulines, and D.S. Stoffer Introduction to Optimization Methods and Their Applications in Statistics B.S. Everitt Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Second Edition J.J. Faraway
- 9. Linear Models with R, Second Edition J.J. Faraway A Course in Large Sample Theory T.S. Ferguson Multivariate Statistics: A Practical Approach B. Flury and H. Riedwyl Readings in Decision Analysis S. French Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data M. Friendly and D. Meyer Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition D. Gamerman and H.F. Lopes Bayesian Data Analysis, Third Edition A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, and D.B. Rubin Multivariate Analysis of Variance and Repeated Measures: A Practical Approach for Behavioural Scientists D.J. Hand and C.C.Taylor Practical Longitudinal Data Analysis D.J. Hand and M. Crowder Logistic Regression Models J.M. Hilbe Richly Parameterized Linear Models: Additive,Time Series, and Spatial Models Using Random Effects J.S. Hodges Statistics for Epidemiology N.P. Jewell Stochastic Processes: An Introduction, Second Edition P.W. Jones and P. Smith The Theory of Linear Models B. Jørgensen Pragmatics of Uncertainty J.B. Kadane Principles of Uncertainty J.B. Kadane Graphics for Statistics and Data Analysis with R K.J. Keen Mathematical Statistics K. Knight Introduction to Multivariate Analysis: Linear and Nonlinear Modeling S. Konishi Nonparametric Methods in Statistics with SAS Applications O. Korosteleva Modeling and Analysis of Stochastic Systems, Second Edition V.G. Kulkarni Exercises and Solutions in Biostatistical Theory L.L. Kupper, B.H. Neelon, and S.M. O’Brien Exercises and Solutions in Statistical Theory L.L. Kupper, B.H. Neelon, and S.M. O’Brien Design and Analysis of Experiments with R J. Lawson Design and Analysis of Experiments with SAS J. Lawson A Course in Categorical Data Analysis T. Leonard Statistics for Accountants S. Letchford Introduction to the Theory of Statistical Inference H. Liero and S. Zwanzig Statistical Theory, Fourth Edition B.W. Lindgren Stationary Stochastic Processes:Theory and Applications G. Lindgren Statistics for Finance E. Lindström, H. Madsen, and J. N. Nielsen The BUGS Book: A Practical Introduction to Bayesian Analysis D. Lunn, C. Jackson, N. Best, A.Thomas, and D. Spiegelhalter Introduction to General and Generalized Linear Models H. Madsen and P.Thyregod Time Series Analysis H. Madsen Pólya Urn Models H. Mahmoud Randomization, Bootstrap and Monte Carlo Methods in Biology,Third Edition B.F.J. Manly Introduction to Randomized Controlled Clinical Trials, Second Edition J.N.S. Matthews Statistical Rethinking: A Bayesian Course with Examples in R and Stan R. McElreath
- 10. Statistical Methods in Agriculture and Experimental Biology, Second Edition R. Mead, R.N. Curnow, and A.M. Hasted Statistics in Engineering: A Practical Approach A.V. Metcalfe Statistical Inference: An Integrated Approach, Second Edition H. S. Migon, D. Gamerman, and F. Louzada Beyond ANOVA: Basics of Applied Statistics R.G. Miller, Jr. A Primer on Linear Models J.F. Monahan Stochastic Processes: From Applications to Theory P.D Moral and S. Penev Applied Stochastic Modelling, Second Edition B.J.T. Morgan Elements of Simulation B.J.T. Morgan Probability: Methods and Measurement A. O’Hagan Introduction to Statistical Limit Theory A.M. Polansky Applied Bayesian Forecasting and Time Series Analysis A. Pole, M. West, and J. Harrison Statistics in Research and Development, Time Series: Modeling, Computation, and Inference R. Prado and M. West Essentials of Probability Theory for Statisticians M.A. Proschan and P.A. Shaw Introduction to Statistical Process Control P. Qiu Sampling Methodologies with Applications P.S.R.S. Rao A First Course in Linear Model Theory N. Ravishanker and D.K. Dey Essential Statistics, Fourth Edition D.A.G. Rees Stochastic Modeling and Mathematical Statistics: A Text for Statisticians and Quantitative Scientists F.J. Samaniego Statistical Methods for Spatial Data Analysis O. Schabenberger and C.A. Gotway Bayesian Networks: With Examples in R M. Scutari and J.-B. Denis Large Sample Methods in Statistics P.K. Sen and J. da Motta Singer Spatio-Temporal Methods in Environmental Epidemiology G. Shaddick and J.V. Zidek Decision Analysis: A Bayesian Approach J.Q. Smith Analysis of Failure and Survival Data P. J. Smith Applied Statistics: Handbook of GENSTAT Analyses E.J. Snell and H. Simpson Applied Nonparametric Statistical Methods, Fourth Edition P. Sprent and N.C. Smeeton Data Driven Statistical Methods P. Sprent Generalized Linear Mixed Models: Modern Concepts, Methods and Applications W. W. Stroup Survival Analysis Using S: Analysis of Time-to-Event Data M.Tableman and J.S. Kim Applied Categorical and Count Data Analysis W.Tang, H. He, and X.M.Tu Elementary Applications of Probability Theory, Second Edition H.C.Tuckwell Introduction to Statistical Inference and Its Applications with R M.W.Trosset Understanding Advanced Statistical Methods P.H. Westfall and K.S.S. Henning Statistical Process Control:Theory and Practice,Third Edition G.B. Wetherill and D.W. Brown Generalized Additive Models: An Introduction with R S. Wood Epidemiology: Study Design and Data Analysis,Third Edition M. Woodward Practical Data Analysis for Designed Experiments B.S. Yandell
- 11. Texts in Statistical Science Pierre Del Moral University of New South Wales Sydney, Australia and INRIA Sud Ouest Research Center Bordeaux, France Spiridon Penev University of New South Wales Sydney, Australia With illustrations by Timothée Del Moral Stochastic Processes From Applications to Theory
- 12. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20161005 International Standard Book Number-13: 978-1-4987-0183-9 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti- lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy- ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
- 13. To Laurence, Tiffany and Timothée; to Tatiana, Iva and Alexander.
- 15. Contents Introduction xxi I An illustrated guide 1 1 Motivating examples 3 1.1 Lost in the Great Sloan Wall . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Meeting Alice in Wonderland . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 The lucky MIT Blackjack Team . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Kruskal’s magic trap card . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 The magic fern from Daisetsuzan . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 The Kepler-22b Eve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.7 Poisson’s typos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2 Selected topics 25 2.1 Stabilizing populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2 The traps of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3 Casino roulette . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4 Surfing Google’s waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.5 Pinging hackers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3 Computational and theoretical aspects 43 3.1 From Monte Carlo to Los Alamos . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Signal processing and population dynamics . . . . . . . . . . . . . . . . . . 45 3.3 The lost equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.4 Towards a general theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.5 The theory of speculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 II Stochastic simulation 69 4 Simulation toolbox 71 4.1 Inversion technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2 Change of variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3 Rejection techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.4 Sampling probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.4.1 Bayesian inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.4.2 Laplace’s rule of successions . . . . . . . . . . . . . . . . . . . . . . . 79 4.4.3 Fragmentation and coagulation . . . . . . . . . . . . . . . . . . . . . 79 4.5 Conditional probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.5.1 Bayes’ formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.5.2 The regression formula . . . . . . . . . . . . . . . . . . . . . . . . . . 81 ix
- 16. x Contents 4.5.3 Gaussian updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.5.4 Conjugate priors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.6 Spatial Poisson point processes . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.6.1 Some preliminary results . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.6.2 Conditioning principles . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.6.3 Poisson-Gaussian clusters . . . . . . . . . . . . . . . . . . . . . . . . 91 4.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5 Monte Carlo integration 99 5.1 Law of large numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2 Importance sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.2.1 Twisted distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.2.2 Sequential Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.2.3 Tails distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6 Some illustrations 107 6.1 Stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.2 Markov chain models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.3 Black-box type models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.4 Boltzmann-Gibbs measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.4.1 Ising model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.4.2 Sherrington-Kirkpatrick model . . . . . . . . . . . . . . . . . . . . . 111 6.4.3 The traveling salesman model . . . . . . . . . . . . . . . . . . . . . . 111 6.5 Filtering and statistical learning . . . . . . . . . . . . . . . . . . . . . . . . 113 6.5.1 Bayes’ formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.5.2 Singer’s radar model . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 III Discrete time processes 119 7 Markov chains 121 7.1 Description of the models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.2 Elementary transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 7.3 Markov integral operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.4 Equilibrium measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.5 Stochastic matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.6 Random dynamical systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 7.6.1 Linear Markov chain model . . . . . . . . . . . . . . . . . . . . . . . 126 7.6.2 Two-states Markov models . . . . . . . . . . . . . . . . . . . . . . . 127 7.7 Transition diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.8 The tree of outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.9 General state space models . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.10 Nonlinear Markov chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 7.10.1 Self interacting processes . . . . . . . . . . . . . . . . . . . . . . . . 132 7.10.2 Mean field particle models . . . . . . . . . . . . . . . . . . . . . . . . 134 7.10.3 McKean-Vlasov diffusions . . . . . . . . . . . . . . . . . . . . . . . . 135 7.10.4 Interacting jump processes . . . . . . . . . . . . . . . . . . . . . . . 136 7.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
- 17. Contents xi 8 Analysis toolbox 141 8.1 Linear algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 8.1.1 Diagonalisation type techniques . . . . . . . . . . . . . . . . . . . . . 141 8.1.2 Perron Frobenius theorem . . . . . . . . . . . . . . . . . . . . . . . . 143 8.2 Functional analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 8.2.1 Spectral decompositions . . . . . . . . . . . . . . . . . . . . . . . . . 145 8.2.2 Total variation norms . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.2.3 Contraction inequalities . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.2.4 Poisson equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 8.2.5 V-norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 8.2.6 Geometric drift conditions . . . . . . . . . . . . . . . . . . . . . . . . 160 8.2.7 V -norm contractions . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.3 Stochastic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8.3.1 Coupling techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8.3.1.1 The total variation distance . . . . . . . . . . . . . . . . . . 166 8.3.1.2 Wasserstein metric . . . . . . . . . . . . . . . . . . . . . . . 169 8.3.2 Stopping times and coupling . . . . . . . . . . . . . . . . . . . . . . 172 8.3.3 Strong stationary times . . . . . . . . . . . . . . . . . . . . . . . . . 173 8.3.4 Some illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 8.3.4.1 Minorization condition and coupling . . . . . . . . . . . . . 174 8.3.4.2 Markov chains on complete graphs . . . . . . . . . . . . . . 176 8.3.4.3 A Kruskal random walk . . . . . . . . . . . . . . . . . . . . 177 8.4 Martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 8.4.1 Some preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 8.4.2 Applications to Markov chains . . . . . . . . . . . . . . . . . . . . . 183 8.4.2.1 Martingales with fixed terminal values . . . . . . . . . . . . 183 8.4.2.2 Doeblin-Itō formula . . . . . . . . . . . . . . . . . . . . . . 184 8.4.2.3 Occupation measures . . . . . . . . . . . . . . . . . . . . . 185 8.4.3 Optional stopping theorems . . . . . . . . . . . . . . . . . . . . . . . 187 8.4.4 A gambling model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 8.4.4.1 Fair games . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.4.4.2 Unfair games . . . . . . . . . . . . . . . . . . . . . . . . . . 193 8.4.5 Maximal inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 8.4.6 Limit theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 8.5 Topological aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 8.5.1 Irreducibility and aperiodicity . . . . . . . . . . . . . . . . . . . . . . 203 8.5.2 Recurrent and transient states . . . . . . . . . . . . . . . . . . . . . 206 8.5.3 Continuous state spaces . . . . . . . . . . . . . . . . . . . . . . . . . 210 8.5.4 Path space models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 8.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 9 Computational toolbox 221 9.1 A weak ergodic theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 9.2 Some illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 9.2.1 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 224 9.2.2 Gaussian subset shaker . . . . . . . . . . . . . . . . . . . . . . . . . 225 9.2.3 Exploration of the unit disk . . . . . . . . . . . . . . . . . . . . . . . 226 9.3 Markov Chain Monte Carlo methods . . . . . . . . . . . . . . . . . . . . . 226 9.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 9.3.2 Metropolis and Hastings models . . . . . . . . . . . . . . . . . . . . 227 9.3.3 Gibbs-Glauber dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 229
- 18. xii Contents 9.3.4 Propp and Wilson sampler . . . . . . . . . . . . . . . . . . . . . . . 233 9.4 Time inhomogeneous MCMC models . . . . . . . . . . . . . . . . . . . . . 236 9.4.1 Simulated annealing algorithm . . . . . . . . . . . . . . . . . . . . . 236 9.4.2 A perfect sampling algorithm . . . . . . . . . . . . . . . . . . . . . . 237 9.5 Feynman-Kac path integration . . . . . . . . . . . . . . . . . . . . . . . . . 239 9.5.1 Weighted Markov chains . . . . . . . . . . . . . . . . . . . . . . . . . 239 9.5.2 Evolution equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 9.5.3 Particle absorption models . . . . . . . . . . . . . . . . . . . . . . . 242 9.5.4 Doob h-processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 9.5.5 Quasi-invariant measures . . . . . . . . . . . . . . . . . . . . . . . . 245 9.5.6 Cauchy problems with terminal conditions . . . . . . . . . . . . . . . 247 9.5.7 Dirichlet-Poisson problems . . . . . . . . . . . . . . . . . . . . . . . 248 9.5.8 Cauchy-Dirichlet-Poisson problems . . . . . . . . . . . . . . . . . . . 250 9.6 Feynman-Kac particle methodology . . . . . . . . . . . . . . . . . . . . . . 252 9.6.1 Mean field genetic type particle models . . . . . . . . . . . . . . . . 252 9.6.2 Path space models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 9.6.3 Backward integration . . . . . . . . . . . . . . . . . . . . . . . . . . 255 9.6.4 A random particle matrix model . . . . . . . . . . . . . . . . . . . . 257 9.6.5 A conditional formula for ancestral trees . . . . . . . . . . . . . . . . 258 9.7 Particle Markov chain Monte Carlo methods . . . . . . . . . . . . . . . . . 260 9.7.1 Many-body Feynman-Kac measures . . . . . . . . . . . . . . . . . . 260 9.7.2 A particle Metropolis-Hastings model . . . . . . . . . . . . . . . . . 261 9.7.3 Duality formulae for many-body models . . . . . . . . . . . . . . . . 262 9.7.4 A couple particle Gibbs samplers . . . . . . . . . . . . . . . . . . . . 266 9.8 Quenched and annealed measures . . . . . . . . . . . . . . . . . . . . . . . 267 9.8.1 Feynman-Kac models . . . . . . . . . . . . . . . . . . . . . . . . . . 267 9.8.2 Particle Gibbs models . . . . . . . . . . . . . . . . . . . . . . . . . . 269 9.8.3 Particle Metropolis-Hastings models . . . . . . . . . . . . . . . . . . 271 9.9 Some application domains . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 9.9.1 Interacting MCMC algorithms . . . . . . . . . . . . . . . . . . . . . 272 9.9.2 Nonlinear filtering models . . . . . . . . . . . . . . . . . . . . . . . . 276 9.9.3 Markov chain restrictions . . . . . . . . . . . . . . . . . . . . . . . . 276 9.9.4 Self avoiding walks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 9.9.5 Twisted measure importance sampling . . . . . . . . . . . . . . . . . 279 9.9.6 Kalman-Bucy filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 9.9.6.1 Forward filters . . . . . . . . . . . . . . . . . . . . . . . . . 280 9.9.6.2 Backward filters . . . . . . . . . . . . . . . . . . . . . . . . 281 9.9.6.3 Ensemble Kalman filters . . . . . . . . . . . . . . . . . . . 283 9.9.6.4 Interacting Kalman filters . . . . . . . . . . . . . . . . . . . 285 9.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 IV Continuous time processes 297 10 Poisson processes 299 10.1 A counting process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 10.2 Memoryless property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 10.3 Uniform random times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 10.4 Doeblin-Itō formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 10.5 Bernoulli process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 10.6 Time inhomogeneous models . . . . . . . . . . . . . . . . . . . . . . . . . . 306 10.6.1 Description of the models . . . . . . . . . . . . . . . . . . . . . . . . 306
- 19. Contents xiii 10.6.2 Poisson thinning simulation . . . . . . . . . . . . . . . . . . . . . . . 309 10.6.3 Geometric random clocks . . . . . . . . . . . . . . . . . . . . . . . . 309 10.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 11 Markov chain embeddings 313 11.1 Homogeneous embeddings . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 11.1.1 Description of the models . . . . . . . . . . . . . . . . . . . . . . . . 313 11.1.2 Semigroup evolution equations . . . . . . . . . . . . . . . . . . . . . 314 11.2 Some illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 11.2.1 A two-state Markov process . . . . . . . . . . . . . . . . . . . . . . . 317 11.2.2 Matrix valued equations . . . . . . . . . . . . . . . . . . . . . . . . . 318 11.2.3 Discrete Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 11.3 Spatially inhomogeneous models . . . . . . . . . . . . . . . . . . . . . . . . 322 11.3.1 Explosion phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . 324 11.3.2 Finite state space models . . . . . . . . . . . . . . . . . . . . . . . . 328 11.4 Time inhomogeneous models . . . . . . . . . . . . . . . . . . . . . . . . . . 329 11.4.1 Description of the models . . . . . . . . . . . . . . . . . . . . . . . . 329 11.4.2 Poisson thinning models . . . . . . . . . . . . . . . . . . . . . . . . . 331 11.4.3 Exponential and geometric clocks . . . . . . . . . . . . . . . . . . . . 332 11.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 12 Jump processes 337 12.1 A class of pure jump models . . . . . . . . . . . . . . . . . . . . . . . . . . 337 12.2 Semigroup evolution equations . . . . . . . . . . . . . . . . . . . . . . . . . 338 12.3 Approximation schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 12.4 Sum of generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 12.5 Doob-Meyer decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . 344 12.5.1 Discrete time models . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 12.5.2 Continuous time martingales . . . . . . . . . . . . . . . . . . . . . . 346 12.5.3 Optional stopping theorems . . . . . . . . . . . . . . . . . . . . . . . 349 12.6 Doeblin-Itō-Taylor formulae . . . . . . . . . . . . . . . . . . . . . . . . . . 350 12.7 Stability properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 12.7.1 Invariant measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 12.7.2 Dobrushin contraction properties . . . . . . . . . . . . . . . . . . . . 353 12.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 13 Piecewise deterministic processes 363 13.1 Dynamical systems basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 13.1.1 Semigroup and flow maps . . . . . . . . . . . . . . . . . . . . . . . . 363 13.1.2 Time discretization schemes . . . . . . . . . . . . . . . . . . . . . . . 366 13.2 Piecewise deterministic jump models . . . . . . . . . . . . . . . . . . . . . . 367 13.2.1 Excursion valued Markov chains . . . . . . . . . . . . . . . . . . . . 367 13.2.2 Evolution semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . 369 13.2.3 Infinitesimal generators . . . . . . . . . . . . . . . . . . . . . . . . . 371 13.2.4 Fokker-Planck equation . . . . . . . . . . . . . . . . . . . . . . . . . 372 13.2.5 A time discretization scheme . . . . . . . . . . . . . . . . . . . . . . 373 13.2.6 Doeblin-Itō-Taylor formulae . . . . . . . . . . . . . . . . . . . . . . . 376 13.3 Stability properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 13.3.1 Switching processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 13.3.2 Invariant measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 13.4 An application to Internet architectures . . . . . . . . . . . . . . . . . . . . 379
- 20. xiv Contents 13.4.1 The transmission control protocol . . . . . . . . . . . . . . . . . . . 379 13.4.2 Regularity and stability properties . . . . . . . . . . . . . . . . . . . 381 13.4.3 The limiting distribution . . . . . . . . . . . . . . . . . . . . . . . . 383 13.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 14 Diffusion processes 393 14.1 Brownian motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 14.1.1 Discrete vs continuous time models . . . . . . . . . . . . . . . . . . . 393 14.1.2 Evolution semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . 395 14.1.3 The heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 14.1.4 Doeblin-Itō-Taylor formula . . . . . . . . . . . . . . . . . . . . . . . 398 14.2 Stochastic differential equations . . . . . . . . . . . . . . . . . . . . . . . . 401 14.2.1 Diffusion processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 14.2.2 Doeblin-Itō differential calculus . . . . . . . . . . . . . . . . . . . . . 402 14.3 Evolution equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 14.3.1 Fokker-Planck equation . . . . . . . . . . . . . . . . . . . . . . . . . 405 14.3.2 Weak approximation processes . . . . . . . . . . . . . . . . . . . . . 406 14.3.3 A backward stochastic differential equation . . . . . . . . . . . . . . 408 14.4 Multidimensional diffusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 14.4.1 Multidimensional stochastic differential equations . . . . . . . . . . . 409 14.4.2 An integration by parts formula . . . . . . . . . . . . . . . . . . . . 411 14.4.3 Laplacian and orthogonal transformations . . . . . . . . . . . . . . . 412 14.4.4 Fokker-Planck equation . . . . . . . . . . . . . . . . . . . . . . . . . 413 14.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 15 Jump diffusion processes 425 15.1 Piecewise diffusion processes . . . . . . . . . . . . . . . . . . . . . . . . . . 425 15.2 Evolution semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 15.3 Doeblin-Itō formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 15.4 Fokker-Planck equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 15.5 An abstract class of stochastic processes . . . . . . . . . . . . . . . . . . . . 434 15.5.1 Generators and carré du champ operators . . . . . . . . . . . . . . . 434 15.5.2 Perturbation formulae . . . . . . . . . . . . . . . . . . . . . . . . . . 437 15.6 Jump diffusion processes with killing . . . . . . . . . . . . . . . . . . . . . 439 15.6.1 Feynman-Kac semigroups . . . . . . . . . . . . . . . . . . . . . . . . 439 15.6.2 Cauchy problems with terminal conditions . . . . . . . . . . . . . . . 440 15.6.3 Dirichlet-Poisson problems . . . . . . . . . . . . . . . . . . . . . . . 442 15.6.4 Cauchy-Dirichlet-Poisson problems . . . . . . . . . . . . . . . . . . . 447 15.7 Some illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450 15.7.1 One-dimensional Dirichlet-Poisson problems . . . . . . . . . . . . . . 450 15.7.2 A backward stochastic differential equation . . . . . . . . . . . . . . 451 15.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 16 Nonlinear jump diffusion processes 463 16.1 Nonlinear Markov processes . . . . . . . . . . . . . . . . . . . . . . . . . . 463 16.1.1 Pure diffusion models . . . . . . . . . . . . . . . . . . . . . . . . . . 463 16.1.2 Burgers equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464 16.1.3 Feynman-Kac jump type models . . . . . . . . . . . . . . . . . . . . 466 16.1.4 A jump type Langevin model . . . . . . . . . . . . . . . . . . . . . . 467 16.2 Mean field particle models . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 16.3 Some application domains . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
- 21. Contents xv 16.3.1 Fouque-Sun systemic risk model . . . . . . . . . . . . . . . . . . . . 470 16.3.2 Burgers equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 16.3.3 Langevin-McKean-Vlasov model . . . . . . . . . . . . . . . . . . . . 472 16.3.4 Dyson equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 16.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 17 Stochastic analysis toolbox 481 17.1 Time changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 17.2 Stability properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 17.3 Some illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 17.3.1 Gradient flow processes . . . . . . . . . . . . . . . . . . . . . . . . . 483 17.3.2 One-dimensional diffusions . . . . . . . . . . . . . . . . . . . . . . . 484 17.4 Foster-Lyapunov techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 485 17.4.1 Contraction inequalities . . . . . . . . . . . . . . . . . . . . . . . . . 485 17.4.2 Minorization properties . . . . . . . . . . . . . . . . . . . . . . . . . 486 17.5 Some applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 17.5.1 Ornstein-Uhlenbeck processes . . . . . . . . . . . . . . . . . . . . . . 487 17.5.2 Stochastic gradient processes . . . . . . . . . . . . . . . . . . . . . . 487 17.5.3 Langevin diffusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 17.6 Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 17.6.1 Hilbert spaces and Schauder bases . . . . . . . . . . . . . . . . . . . 490 17.6.2 Spectral decompositions . . . . . . . . . . . . . . . . . . . . . . . . . 493 17.6.3 Poincaré inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 17.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 18 Path space measures 501 18.1 Pure jump models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501 18.1.1 Likelihood functionals . . . . . . . . . . . . . . . . . . . . . . . . . . 504 18.1.2 Girsanov’s transformations . . . . . . . . . . . . . . . . . . . . . . . 505 18.1.3 Exponential martingales . . . . . . . . . . . . . . . . . . . . . . . . . 506 18.2 Diffusion models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 18.2.1 Wiener measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 18.2.2 Path space diffusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 18.2.3 Girsanov transformations . . . . . . . . . . . . . . . . . . . . . . . . 509 18.3 Exponential change twisted measures . . . . . . . . . . . . . . . . . . . . . 512 18.3.1 Diffusion processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 18.3.2 Pure jump processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 18.4 Some illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 18.4.1 Risk neutral financial markets . . . . . . . . . . . . . . . . . . . . . . 514 18.4.1.1 Poisson markets . . . . . . . . . . . . . . . . . . . . . . . . 514 18.4.1.2 Diffusion markets . . . . . . . . . . . . . . . . . . . . . . . 515 18.4.2 Elliptic diffusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 18.5 Nonlinear filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 18.5.1 Diffusion observations . . . . . . . . . . . . . . . . . . . . . . . . . . 517 18.5.2 Duncan-Zakai equation . . . . . . . . . . . . . . . . . . . . . . . . . 518 18.5.3 Kushner-Stratonovitch equation . . . . . . . . . . . . . . . . . . . . 520 18.5.4 Kalman-Bucy filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 18.5.5 Nonlinear diffusion and ensemble Kalman-Bucy filters . . . . . . . . 523 18.5.6 Robust filtering equations . . . . . . . . . . . . . . . . . . . . . . . . 524 18.5.7 Poisson observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 18.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
- 22. xvi Contents V Processes on manifolds 533 19 A review of differential geometry 535 19.1 Projection operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 19.2 Covariant derivatives of vector fields . . . . . . . . . . . . . . . . . . . . . . 541 19.2.1 First order derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . 543 19.2.2 Second order derivatives . . . . . . . . . . . . . . . . . . . . . . . . . 546 19.3 Divergence and mean curvature . . . . . . . . . . . . . . . . . . . . . . . . 547 19.4 Lie brackets and commutation formulae . . . . . . . . . . . . . . . . . . . . 554 19.5 Inner product derivation formulae . . . . . . . . . . . . . . . . . . . . . . . 556 19.6 Second order derivatives and some trace formulae . . . . . . . . . . . . . . 559 19.7 Laplacian operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 19.8 Ricci curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 19.9 Bochner-Lichnerowicz formula . . . . . . . . . . . . . . . . . . . . . . . . . 568 19.10Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576 20 Stochastic differential calculus on manifolds 579 20.1 Embedded manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 20.2 Brownian motion on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . 581 20.2.1 A diffusion model in the ambient space . . . . . . . . . . . . . . . . 581 20.2.2 The infinitesimal generator . . . . . . . . . . . . . . . . . . . . . . . 583 20.2.3 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . 584 20.3 Stratonovitch differential calculus . . . . . . . . . . . . . . . . . . . . . . . 584 20.4 Projected diffusions on manifolds . . . . . . . . . . . . . . . . . . . . . . . 586 20.5 Brownian motion on orbifolds . . . . . . . . . . . . . . . . . . . . . . . . . 589 20.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591 21 Parametrizations and charts 593 21.1 Differentiable manifolds and charts . . . . . . . . . . . . . . . . . . . . . . 593 21.2 Orthogonal projection operators . . . . . . . . . . . . . . . . . . . . . . . . 596 21.3 Riemannian structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 21.4 First order covariant derivatives . . . . . . . . . . . . . . . . . . . . . . . . 602 21.4.1 Pushed forward functions . . . . . . . . . . . . . . . . . . . . . . . . 602 21.4.2 Pushed forward vector fields . . . . . . . . . . . . . . . . . . . . . . . 604 21.4.3 Directional derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . 606 21.5 Second order covariant derivative . . . . . . . . . . . . . . . . . . . . . . . 609 21.5.1 Tangent basis functions . . . . . . . . . . . . . . . . . . . . . . . . . 609 21.5.2 Composition formulae . . . . . . . . . . . . . . . . . . . . . . . . . . 612 21.5.3 Hessian operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613 21.6 Bochner-Lichnerowicz formula . . . . . . . . . . . . . . . . . . . . . . . . . 617 21.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 22 Stochastic calculus in chart spaces 629 22.1 Brownian motion on Riemannian manifolds . . . . . . . . . . . . . . . . . . 629 22.2 Diffusions on chart spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631 22.3 Brownian motion on spheres . . . . . . . . . . . . . . . . . . . . . . . . . . 632 22.3.1 The unit circle S = S1 ⊂ R2 . . . . . . . . . . . . . . . . . . . . . . . 632 22.3.2 The unit sphere S = S2 ⊂ R3 . . . . . . . . . . . . . . . . . . . . . . 633 22.4 Brownian motion on the torus . . . . . . . . . . . . . . . . . . . . . . . . . 634 22.5 Diffusions on the simplex . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635 22.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
- 23. Contents xvii 23 Some analytical aspects 639 23.1 Geodesics and the exponential map . . . . . . . . . . . . . . . . . . . . . . 639 23.2 Taylor expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 23.3 Integration on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645 23.3.1 The volume measure on the manifold . . . . . . . . . . . . . . . . . . 645 23.3.2 Wedge product and volume forms . . . . . . . . . . . . . . . . . . . 648 23.3.3 The divergence theorem . . . . . . . . . . . . . . . . . . . . . . . . . 650 23.4 Gradient flow models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657 23.4.1 Steepest descent model . . . . . . . . . . . . . . . . . . . . . . . . . 657 23.4.2 Euclidian state spaces . . . . . . . . . . . . . . . . . . . . . . . . . . 658 23.5 Drift changes and irreversible Langevin diffusions . . . . . . . . . . . . . . 659 23.5.1 Langevin diffusions on closed manifolds . . . . . . . . . . . . . . . . 661 23.5.2 Riemannian Langevin diffusions . . . . . . . . . . . . . . . . . . . . . 662 23.6 Metropolis-adjusted Langevin models . . . . . . . . . . . . . . . . . . . . . 665 23.7 Stability and some functional inequalities . . . . . . . . . . . . . . . . . . . 666 23.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669 24 Some illustrations 673 24.1 Prototype manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673 24.1.1 The circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673 24.1.2 The 2-sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674 24.1.3 The torus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678 24.2 Information theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681 24.2.1 Nash embedding theorem . . . . . . . . . . . . . . . . . . . . . . . . 681 24.2.2 Distribution manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . 682 24.2.3 Bayesian statistical manifolds . . . . . . . . . . . . . . . . . . . . . . 683 24.2.4 Cramer-Rao lower bound . . . . . . . . . . . . . . . . . . . . . . . . 685 24.2.5 Some illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685 24.2.5.1 Boltzmann-Gibbs measures . . . . . . . . . . . . . . . . . . 685 24.2.5.2 Multivariate normal distributions . . . . . . . . . . . . . . 686 VI Some application areas 691 25 Simple random walks 693 25.1 Random walk on lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693 25.1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693 25.1.2 Dimension 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693 25.1.3 Dimension 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694 25.1.4 Dimension d ≥ 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694 25.2 Random walks on graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694 25.3 Simple exclusion process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695 25.4 Random walks on the circle . . . . . . . . . . . . . . . . . . . . . . . . . . . 695 25.4.1 Markov chain on cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 695 25.4.2 Markov chain on circle . . . . . . . . . . . . . . . . . . . . . . . . . . 696 25.4.3 Spectral decomposition . . . . . . . . . . . . . . . . . . . . . . . . . 696 25.5 Random walk on hypercubes . . . . . . . . . . . . . . . . . . . . . . . . . . 697 25.5.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697 25.5.2 A macroscopic model . . . . . . . . . . . . . . . . . . . . . . . . . . 698 25.5.3 A lazy random walk . . . . . . . . . . . . . . . . . . . . . . . . . . . 698 25.6 Urn processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 25.6.1 Ehrenfest model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699
- 24. xviii Contents 25.6.2 Pólya urn model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700 25.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701 26 Iterated random functions 705 26.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 26.2 A motivating example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707 26.3 Uniform selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708 26.3.1 An ancestral type evolution model . . . . . . . . . . . . . . . . . . . 708 26.3.2 An absorbed Markov chain . . . . . . . . . . . . . . . . . . . . . . . 709 26.4 Shuffling cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 26.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 26.4.2 The top-in-at-random shuffle . . . . . . . . . . . . . . . . . . . . . . 712 26.4.3 The random transposition shuffle . . . . . . . . . . . . . . . . . . . . 713 26.4.4 The riffle shuffle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716 26.5 Fractal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 26.5.1 Exploration of Cantor’s discontinuum . . . . . . . . . . . . . . . . . 720 26.5.2 Some fractal images . . . . . . . . . . . . . . . . . . . . . . . . . . . 723 26.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 27 Computational and statistical physics 731 27.1 Molecular dynamics simulation . . . . . . . . . . . . . . . . . . . . . . . . . 731 27.1.1 Newton’s second law of motion . . . . . . . . . . . . . . . . . . . . . 731 27.1.2 Langevin diffusion processes . . . . . . . . . . . . . . . . . . . . . . . 734 27.2 Schrödinger equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737 27.2.1 A physical derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 737 27.2.2 Feynman-Kac formulation . . . . . . . . . . . . . . . . . . . . . . . . 739 27.2.3 Bra-kets and path integral formalism . . . . . . . . . . . . . . . . . . 742 27.2.4 Spectral decompositions . . . . . . . . . . . . . . . . . . . . . . . . . 743 27.2.5 The harmonic oscillator . . . . . . . . . . . . . . . . . . . . . . . . . 745 27.2.6 Diffusion Monte Carlo models . . . . . . . . . . . . . . . . . . . . . . 748 27.3 Interacting particle systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 749 27.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749 27.3.2 Contact process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751 27.3.3 Voter process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751 27.3.4 Exclusion process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752 27.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753 28 Dynamic population models 759 28.1 Discrete time birth and death models . . . . . . . . . . . . . . . . . . . . . 759 28.2 Continuous time models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762 28.2.1 Birth and death generators . . . . . . . . . . . . . . . . . . . . . . . 762 28.2.2 Logistic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762 28.2.3 Epidemic model with immunity . . . . . . . . . . . . . . . . . . . . . 764 28.2.4 Lotka-Volterra predator-prey stochastic model . . . . . . . . . . . . 765 28.2.5 Moran genetic model . . . . . . . . . . . . . . . . . . . . . . . . . . . 768 28.3 Genetic evolution models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769 28.4 Branching processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 770 28.4.1 Birth and death models with linear rates . . . . . . . . . . . . . . . 770 28.4.2 Discrete time branching processes . . . . . . . . . . . . . . . . . . . 772 28.4.3 Continuous time branching processes . . . . . . . . . . . . . . . . . . 773 28.4.3.1 Absorption-death process . . . . . . . . . . . . . . . . . . . 774
- 25. Contents xix 28.4.3.2 Birth type branching process . . . . . . . . . . . . . . . . . 775 28.4.3.3 Birth and death branching processes . . . . . . . . . . . . . 777 28.4.3.4 Kolmogorov-Petrovskii-Piskunov equation . . . . . . . . . . 778 28.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 780 29 Gambling, ranking and control 787 29.1 Google page rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787 29.2 Gambling betting systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 788 29.2.1 Martingale systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 788 29.2.2 St. Petersburg martingales . . . . . . . . . . . . . . . . . . . . . . . 789 29.2.3 Conditional gains and losses . . . . . . . . . . . . . . . . . . . . . . . 791 29.2.3.1 Conditional gains . . . . . . . . . . . . . . . . . . . . . . . 791 29.2.3.2 Conditional losses . . . . . . . . . . . . . . . . . . . . . . . 791 29.2.4 Bankroll management . . . . . . . . . . . . . . . . . . . . . . . . . . 792 29.2.5 Grand martingale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794 29.2.6 D’Alembert martingale . . . . . . . . . . . . . . . . . . . . . . . . . 794 29.2.7 Whittacker martingale . . . . . . . . . . . . . . . . . . . . . . . . . . 796 29.3 Stochastic optimal control . . . . . . . . . . . . . . . . . . . . . . . . . . . 797 29.3.1 Bellman equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797 29.3.2 Control dependent value functions . . . . . . . . . . . . . . . . . . . 802 29.3.3 Continuous time models . . . . . . . . . . . . . . . . . . . . . . . . . 804 29.4 Optimal stopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807 29.4.1 Games with fixed terminal condition . . . . . . . . . . . . . . . . . . 807 29.4.2 Snell envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809 29.4.3 Continuous time models . . . . . . . . . . . . . . . . . . . . . . . . . 811 29.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812 30 Mathematical finance 821 30.1 Stock price models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 821 30.1.1 Up and down martingales . . . . . . . . . . . . . . . . . . . . . . . . 821 30.1.2 Cox-Ross-Rubinstein model . . . . . . . . . . . . . . . . . . . . . . . 824 30.1.3 Black-Scholes-Merton model . . . . . . . . . . . . . . . . . . . . . . . 825 30.2 European option pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826 30.2.1 Call and put options . . . . . . . . . . . . . . . . . . . . . . . . . . . 826 30.2.2 Self-financing portfolios . . . . . . . . . . . . . . . . . . . . . . . . . 827 30.2.3 Binomial pricing technique . . . . . . . . . . . . . . . . . . . . . . . 828 30.2.4 Black-Scholes-Merton pricing model . . . . . . . . . . . . . . . . . . 830 30.2.5 Black-Scholes partial differential equation . . . . . . . . . . . . . . . 831 30.2.6 Replicating portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . 832 30.2.7 Option price and hedging computations . . . . . . . . . . . . . . . . 833 30.2.8 A numerical illustration . . . . . . . . . . . . . . . . . . . . . . . . . 834 30.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835 Bibliography 839 Index 855
- 26. Discovering Diverse Content Through Random Scribd Documents
- 28. 2 —— Profile of a Kingfish “The iniquity of oblivion blindly scattereth her poppy, and deals with the memory of men without distinction to merit of perpetuity.” ——SIR THOMAS BROWNE One day some of the VIP’s of the Long political hierarchy were gathered in the office of Governor Oscar Allen when a matter of legislative procedure was under discussion. It is worth noting for the record that the Governor’s chair was occupied by Senator Huey Long. Governor Allen sat at one side of his desk. The names of the others do not matter. Among them were highway commissioners, a state purchasing agent, floor leaders from House and Senate, the head of an upstate levee board, and the like. Huey was issuing orders and lost his temper over the apparent inattention of some conferees, who were conducting a low-voiced conversation in a corner of the room. “Shut up, damn it!” he shouted suddenly. “Shut up and listen to me. This is the Kingfish of the Lodge talking!” From that day on he was “Kingfish.” Even Franklin Roosevelt, telephoning him from New York during the hectic maneuvering which preceded that summer’s Democratic national convention, greeted him with the words: “Hello, Kingfish!” The self-proclaimed Kingfish was named Huey Pierce Long at his birth on August 30, 1893, the third of four sons born to Huey Pierce Long, Sr., and Caledonia Tyson Long. The family farm was near
- 29. Winnfield, and by the standards of that place and time the Longs were well off; not wealthy, to be sure, but never in want. Winnfield, seat of Winn parish, is a small wholly rural community not far from the center of the state. “Just near the center of the state?” Westbrook Pegler once asked Senator Long incredulously after watching him put his legislative trained seals through their paces. “Just near the center of the state? I’m surprised you haven’t had the legislature declare it to be the center of the state.” Scholastically, Huey did not distinguish himself, and he took no part in athletics, lacking the physical pugnacity that is the heritage of most young males. His brother Earl, two years younger than Huey, frequently asserted that “I had to do all Huey’s fighting for him.” But as long as he remained in high school (he left after a disagreement with the principal and before graduation) he was the best debater that institution ever numbered among its pupils. His first essay into the realm of self-support came at age fourteen, when he loaded a rented buggy with books and drove about the countryside selling these at public auction. In doing so he laid the foundation for what became the largest personal acquaintance any one individual ever had among the farm folk of Louisiana. “I’d never stay at a hotel, even later on, when I was out selling Cottolene or baking powder or lamp chimneys or whatever,” he would boast. “I always drove out beyond town to a farmhouse where they’d take me in and put up my horse, and I would pay them something and put in the evening talking to them, and later I would make it my business to drop those folks a post card so they’d be sure to remember me.” At summer’s end he entered Oklahoma University at Norman, hoping to work his way through law school as weekend drummer for the Kaye Dawson wholesale grocery. That did not work out. After a heated disagreement with the head of the business he returned to Louisiana and became a door-to-door salesman for Cottolene. In glorifying this product he held cake-baking contests here, there, and yonder.
- 30. “My job was to convince those women they could fry chickens, steaks, or fish in something else besides hog lard, and bake a cake using something else besides cow butter,” he explained. “I would quote the Bible to them where it said not to use any part of the flesh of swine, and if I couldn’t convince them out of the Bible, I would go into the kitchen and bake a cake for them myself.” First prize for one of his cake-baking contests in Shreveport was awarded to pretty Rose McConnell. Not long thereafter, she and Huey were married. With all his savings and a substantial loan from his older brother Julius, he managed to finance nearly a year of special study at Tulane University’s law school in New Orleans. He and Rose shared a room in a private home not far from the university, where among other furnishings, a rented typewriter was installed. Young Mr. Long would bring home a law book, drive through it in furious haste while his phenomenally retentive memory seized every really salient detail, “and then I would abstract the hell out of it, dictating to my wife, who would type it out for me.” With barely enough money for housing, carfare, short rations, and such essentials as paper and pencils, it is none the less probable that these were the least troubled, most nearly contented and carefree days the couple would ever know. Before year’s end he was admitted to the bar, and returned to Winnfield with Rose to begin practice. He soon realized that despite local successes, the ambitious goals he had set for himself could be attained only in a much larger field. So he moved to Shreveport, which was just at the threshold of a tremendous boom following the discovery of oil in the nearby Pine Island areas. By accepting royalty shares and acreage allotments for legal services in examining titles and the like, Huey was on the threshold of becoming very wealthy, when he and the other Pine Islanders discovered that they could not send their black gold to market unless they sold it at ruinously low prices to owners of the only available pipeline. Long’s implacable hostility toward the Standard Oil Company had its inception then and there.
- 31. As first step in a campaign to have pipelines declared common carriers, he became a candidate for the Railroad (now Public Service) Commission and was elected. The brothers Long presented a solid front on this occasion, Julius and Earl working like beavers to help Huey win. George (“Shan”) had moved to Oklahoma by that time to practice dentistry. Only once thereafter were they politically united, and that was when Huey ran for governor in 1928. Commissioner Long made his first state-wide stump speech the following year at a rally and picnic which six candidates for governor had been called to address. He had not been invited to speak, but asked permission to say a few words—and stole the show! One must picture him: a young man whose bizarre garb was accented by the fact that since he was wearing a bow tie, the gleaming stickpin with its big diamond sparkled from the otherwise bare band of his shirt front. The unruly forelock of rusty brown hair, a fleshy, cleft chin, and a general air of earnest fury all radiated anger. His blistering denunciation of the then governor as a pliant tool of the Standard Oil Company, and his attack on the state fire marshal, an anti-Long politico from Winnfield, as “the official barfly of the state of Louisiana” captured all the next day’s headlines. Thenceforth the pattern of his future was set. He continued his attacks on trusts and large corporations, certain that this would enlarge his image as defender and champion of the downtrodden “pore folks.” His assaults became so intemperate that in 1921, Governor John M. Parker filed an affidavit against him with the Baton Rouge district attorney, and thus brought about his arrest and trial on charges of criminal libel. His attorneys were his brother Julius, Judge James G. Palmer of Shreveport, and Judge Robert R. Reid of Amite. He was found guilty, but his reputation as a pitiless opponent was already so great that only a token sentence was imposed: one hour’s detention, which he served in the Judge’s chambers, and a one-dollar fine. He was so delighted by the outcome that he gave his youngest son, born that day, the names of his attorneys: Palmer Reid Long. Also, some years later, he saw to it that the judge who had imposed the token penalties was elected to the state supreme court.
- 32. Continuing his onslaughts against millionaires and monopolies, he ran for governor in 1924 on a platform of taxing the owners of great fortunes to aid the underprivileged in their struggle for a reasonable share of the better life: education for their children, medical care for all who could not afford to pay, and some sort of economic security for all who toiled, be it in factory, market place, mine, or farm. He now inveighed against Wall Street as a whole, not merely against isolated corporations as before. The Mellon fortune and the House of Morgan came in for their oratorical lumps; but it is a matter of record that later, when Earl and Huey had fallen out, the former testified under oath before a Senate investigating committee that he had seen his brother accept $10,000 from an official of the Electric Bond and Share Company “in bills so new they looked like they’d just come off the press.” However, from every stump Huey proclaimed that “ninety per cent of this nation’s wealth is in the hands of ten per cent of its people.... The Bible tells us that unless we redistribute the wealth of a country amongst all of the people every so often, that country’s going to smash; but we got too many folks running things in Louisiana and in Washington that think they’re smarter than the Bible.” None the less he ran third in a three-man first primary. In view of the fact that he had no organized backing it must be conceded that it was a close third, an amazing achievement the credit for which must be given to his wide acquaintance among the farm population and the matchless fire of his eloquence. A number of factors contributed to his defeat. One of them undeniably was his refusal, or inability, to recognize that he “could not hold his liquor.” After a convivial evening at a lake-front resort in New Orleans, he drove back to town with his campaign manager at a wildly illicit speed and was promptly halted by a motorcycle officer. His campaign manager hastily explained to the patrolman that the car was his, and that his chauffeur, one Harold Swan, had merely acted under orders. But the fact that Huey Long and Harold Swan in this instance were one and the same came out later, along with accounts of how Huey had gone tipsily from table to table at the Moulin Rouge inviting all and sundry to be his personal guests at his inaugural ball.
- 33. Ordinarily, this might have won him votes in tolerant south Louisiana, where prohibition was regarded as the figment of sick imaginations, like the loup garou. But in south Louisiana he had few backers in that campaign to begin with, being a north Louisiana hillman; and in north Louisiana, where drinking had to be done in secret even before the Volstead Act became nominally the law of the land, such reports were sheer poison. Finally, the weather on election day turned foul. The wretched dirt roads of the hinterlands where Huey’s voting strength was concentrated became impassable, so that many of his supporters could not reach their polling places. But four years later, when he once more ran for governor in yet another three-man race, he barely missed a majority in the first primary. No run-off was held, however, because one of his opponents announced he would throw his support to Long, pulling with him many followers, including a young St. Landry parish physician, Dr. F. Octave Pavy, who had run for lieutenant governor. Under the circumstances a second primary would have been merely an empty gesture of defiance. As governor, he rode roughshod over all opposition to his proposal to furnish free textbooks to every school child, not merely in the public schools, but in the Catholic parochial schools and the posh private academies as well; for a highway-improvement program which he proposed to finance out of increased gasoline taxes. Nor was he one to hide his light under a bushel in pretended modesty. On the contrary, after each success he rang the changes on Jack Horner’s classic “What a good [in the sense of great] boy am I.” Moreover, it made little difference to his devotees whether his promises of still greater benefits for the future, or boasts about the wonders he had already achieved, were based on fact or fiction. By way of illustration: Dr. Arthur Vidrine, a back-country physician, was catapulted into the superintendency of the state’s huge Charity Hospital at New Orleans, and later was additionally made dean of the new state university College of Medicine Long decided to found. Vidrine had won the new governor’s warm regard by captaining the Long cause in Ville Platte, where he was a general practitioner.
- 34. In some quarters there is a disposition to regard Arthur Vidrine as no more than a hack who relied on political manipulation to secure professional advancement. While it is obvious that his original support of, and later complete subservience to, Huey Long brought him extraordinary preferment, it must not be overlooked that in 1920, when he was graduated from Tulane University’s college of medicine, he was a sufficiently brilliant student to be chosen in open, nonpolitical competition for the award of a Rhodes scholarship, and that for two years he took advantage of this grant to pursue his studies abroad. After his return he served for a time as junior intern at New Orleans’ huge Charity Hospital ... and within four years he was made superintendent of that famous institution and dean of his state university’s new medical school, both appointments being conferred on him by newly elected Governor Huey Long, who lost no opportunity to picture his protégé as something of a miracle man in the realm of healing. To an early joint session of the legislature, His Excellency announced that under his administration Dr. Vidrine had reduced cancer mortality at Charity Hospital by one third. This was obvious nonsense. Had it not been, the medical world would long since have beaten a path to the ornamental iron gates of the century-old hospital in quest of further enlightenment. One of the newspapers finally solved the mystery of this miracle of healing. It stemmed solely from a change in the system of tabulating mortality statistics. Calculated on the old basis, the death rate was precisely what it had been before, a little better in some years, a little worse in others. All this was set forth publicly in clear, simple wording. But except for a few of the palace guard, who cynically shrugged the explanation aside, not one of the Long followers accorded it the slightest heed. They and their peerless standard bearer continued to glory in the “fact” that he had reduced Charity’s cancer death rate by a third. This accomplishment was by no means the only one of which young Governor Long boasted. Less tactfully, and certainly less judiciously, he made vainglorious public statements to the effect that
- 35. “I hold all fifty-two cards at Baton Rouge, and shuffle and deal them as I please”; also that he had bought this legislator or that, “like you’d buy a sack of potatoes to be delivered at your gate.” Within a year the House of Representatives impeached him on nine counts. Huey had learned that such a movement was to be launched at a special session in late March of 1929, and sent word to his legislative legions to adjourn sine die before an impeachment resolution could be introduced. But an electric malfunction in the voting machine made it appear that the House voted almost unanimously to adjourn, when in fact opinion was sharply divided. A riot ensued, which was finally quelled when Representative Mason Spencer of Tallulah, a brawny giant, bellowed the words: “In the name of sanity and common sense!” Momentarily this stilled the tumult and Spencer, not an official of the House, but merely one of its members, called the roll himself, by voice, on which tally only seven of the hundred members voted to adjourn. The committee of impeachment managers in the House was headed by Spencer and by his close friend, another huge man, George Perrault of Opelousas. However, the impeachment charges were aborted in the Senate, when Long induced fifteen members of that thirty-nine-man body to sign a round robin to the effect that on technical grounds they would refuse to convict regardless of evidence. Since this was one vote more than enough to block the two-thirds majority needed for conviction, the impeachment charges were dropped. Spencer and Perrault remained inseparable friends, occupying adjacent seats in the House to the day of Perrault’s death during the winter of 1934. On the night of September 8, 1935, Huey stopped to chat momentarily with Spencer, who took occasion to protest against the appointment of Edward Loeb, who had replaced his friend Perrault “All these years I’ve got used to having a man the size of George Perrault sitting next to me,” he complained. “Did you have to make Oscar appoint a pint-size member like Eddie Loeb to sit in his place here?”
- 36. “You remind me,” retorted Long, “of the old nigger woman that was in a bind of some sort, and her boss helped her out, giving her clothes or money or vittles or whatever. So she said to him: ‘Mist’ Pete, you got a white face, fo’ true, but you’s so good you’s bound to have a black heart.’ That’s you, Mason. Your face is white, but you’ve sure enough got a black heart.” A year after the abortive impeachment Long announced he would run for the Senate forthwith, though his gubernatorial tenure would not be terminated for another two years. In this way, he said, he would submit his case to the people. If they elected him, they would thereby express approval of his program. If not, they would elect his opponent, the long-time incumbent senator. Long was elected overwhelmingly, and then went from one political success to another, electing another Winnfieldian, his boyhood chum Oscar Allen, to succeed him as governor, and smashingly defeating a ticket on which his brother Earl was running for lieutenant governor with his brother Julius’ active support. It was later that year that Earl testified against Huey before a Senate committee. In that same year Huey Long entered Arkansas politics. Mrs. Hattie Caraway, widow of Senator Thad Caraway, had been appointed to serve the few remaining months of her husband’s term, then announced as a candidate for re-election. Huey had two reasons for espousing her candidacy. First, she had voted with him for a resolution favoring the limitation of individual incomes by law to a maximum of a million dollars a year. Secondly, the senior senator from Arkansas, Majority Leader Joe T. Robinson, who had turned thumbs down on this resolution, had endorsed one of the candidates opposing Mrs. Caraway’s election. Thirdly, he felt it was time to put the country on notice that Kingfishing could be carried successfully beyond the borders of its home state. Mrs. Caraway was accorded no chance to win. Every organized political group in the state had endorsed one or another of her six opponents, among whom were included a national commander of the American Legion, two former governors, a Supreme Court justice, and other bigwigs. The opening address of the nine-day
- 37. campaign Huey Long waged with Mrs. Caraway was delivered at Magnolia, just north of the Louisiana border. At its close, a dazed local political Pooh-Bah wired a major campaign headquarters in Little Rock: “A tornado just passed through here. Very few trees left standing, and even those are badly scarred up.” It was here that Long first formulated what later became the Share-Our-Wealth clubs’ credo. “In this country,” he proclaimed, “we raise so much food there’d be plenty for all if we never slaughtered another hog or harvested another bushel of grain for the next two years, and yet people are going hungry. We’ve got enough material for clothes if in the next two years we never tanned another hide or raised another lock of cotton, and yet people are going barefoot and naked. Enough houses in this land are standing empty to put a roof over every head at night, and yet people are wandering the highways for lack of shelter.” The remedy he proposed was simple: share our wealth instead of leaving almost all of it in the hands of a greedy few. “All in this living world you’ve got to do,” he insisted, “is to limit individual incomes to one million dollars a year, and fix it so nobody when he dies can leave to any one child more than five million dollars. And let me tell you something: holding one of those birds down to a measly million dollars a year’s no sort of hardship on him. At that rate of income, if he stopped to bathe and shave, he’d be just about five hundred dollars the richer by the time he got his clothes back on. “What we got to do is break up those enormous fortunes like the billion-dollar Mellon estate. By allowing them a million dollars a year for spending-money you’ll agree we wouldn’t be hurting ’em any to speak of. We’d have the balance to distribute amongst all the people, and that would fix things so everybody’d be able to live like he could right now if he made five thousand a year. Yes sir, like he was having five thousand a year and a team of mules to work with, once we share the wealth!” Today it is almost impossible to visualize the effect of so alluring a prospect on a countryside forced at that time to rely on the Red
- 38. Cross for seed corn and sweet-potato slips to assure a winter’s food supply. The rural Negroes in particular, their “furnish” sadly shrunken as a result of the depression, accepted it almost as gospel that Huey Long was promising them five thousand dollars a year and a team of mules. The impact of Long’s oratory was so clearly obvious that a special committee waited on him at Texarkana, where he planned to close the campaign on Saturday night, to ask that he remain in Arkansas over the weekend to address meetings in the tier of counties along the Mississippi River on Monday, the day before the election. He agreed to do this, canceled plans to drive to Shreveport from Texarkana, and drove back to Little Rock instead. Since this left the accompanying newsmen with no grist for the early Monday editions, and since he had been quoting the Bible right and left in his speeches, not to mention the fact that in the glove compartment of his Cadillac a well-thumbed Bible reposed beside a loaded revolver and an atomizer of throat spray, he was asked where he expected to attend church the next morning. “Me go to church?” he inquired incredulously. “Why I haven’t been to a church in so many years I don’t know when.” “But you’re always quoting the Bible and so....” “Bible’s the greatest book ever written,” he interrupted, “but I sure don’t need anybody I can buy for six bits and a chew of tobacco to explain it to me. When I need preachers I buy ’em cheap.” Mrs. Caraway’s first primary victory was a landslide. Well pleased, Huey returned to Louisiana to defeat two-term incumbent Senator Edwin S. Broussard and elect one of his chief attorneys in the impeachment case, John H. Overton, in his stead. It was this election which a Senate committee later investigated to sift allegations of fraud. The investigation was recessed midway to give Senator Long an opportunity to halt a threatened bank run by the simple expedient of having Oscar Allen proclaim Saturday, February 4, a holiday celebrating the fact that sixteen years before, on February 3 and 4, 1917, Woodrow Wilson had severed diplomatic relations with Germany!
- 39. PROCLAMATION STATE OF LOUISIANA EXECUTIVE DEPARTMENT BATON ROUGE Whereas, on the nights of February 3 and 4, 1917, Woodrow Wilson, president of the United States, severed diplomatic relations with the Imperial German government; and Whereas, more than 16 years has intervened before the great American people have turned their eyes back to the lofty ideals of human uplift and new freedom as propounded by Woodrow Wilson; and Whereas, it is now fitting that due recognition be given by the great State of Louisiana in line with the far-reaching principles enunciated by the illustrious southerner who sought to break the fetters of mankind throughout the world; Now, therefore, I, Oscar Kelly Allen, governor of the State of Louisiana, do hereby ordain that Saturday, the fourth day of February, 1933, the 16th anniversary of the severance of diplomatic relations between the United States and the Imperial German government be, and the same is hereby declared, a holiday throughout the State of Louisiana and I do hereby order that all public business, including schools, colleges, banks and other public enterprises be suspended on said day and that the proper ceremonies to commemorate that event be held. In witness whereof I have caused to be affixed the great seal of the State of Louisiana on this, the third day of February, in the year of Our Lord, A. D. 1933.
- 40. This meant that all public offices, schools—and banks—were legally forbidden to open their doors on that Saturday; by Sunday the Federal Reserve authorities had put $20,000,000 at the disposal of the menaced bank and the run which might have spread panic throughout the country died a-borning. However, bank closures on a national scale were thus postponed for only a month. March 4, while Franklin Roosevelt was taking his first oath as president, state after state was ordering its banks to close, as financial consternation (vectored from Detroit, however, and not from New Orleans) stampeded across the land. One of the newly inaugurated President’s first acts—“The only thing we have to fear is fear itself!”—was to order all the nation’s banks to close until individually authorized by executive permit to reopen. But the onus of having initiated the disaster had been averted from Louisiana by Huey’s bizarre bank holiday, and this underscored the fact that for some time past, the number and ratio of bank failures in Louisiana had been far, far below the national average. It also strengthened the growing conviction that Louisiana’s Long was something more than another Southern demagogue like Mississippi’s Bilbo or Texas’ Pa Ferguson. Franklin Roosevelt was probably never under any illusions on that score. He gauged quite correctly the omen of Share-Our-Wealth’s growing strength. It had been blueprinted for all to see when Mrs. Caraway’s candidacy swept the boards in Arkansas, and again when
- 41. this movement, plus the oratorical spell cast by the Louisianian in stumping the Midwestern prairie states, carried them for Roosevelt later that same autumn. According to Long’s subsequent diatribes, he had campaigned thus for “Roosevelt the Little” on the express understanding that the president-to-be would back the program for limiting individual incomes and bequests by statute. There is ample ground for the belief that Long was secretly gratified when he realized that the New Dealers would have none of this proposal. The issue which had served him so well in the past could thus be turned against Roosevelt four years later, when Long planned to enter the lists as a rival candidate for the world’s loftiest office. Publicly, to be sure, he professed himself outraged by “this double cross,” bolted the administration ranks once more, repeated an earlier, defiant fulmination to the effect that if the New Dealers wished to withhold control over Louisiana’s federal appointments from him, they could take this patronage and “go slap dab to hell with it.” Roosevelt and his fidus Achates, Harry Hopkins, took him at his word, and gave the anti-Long faction, headed by Mayor Walmsley of New Orleans, a controlling voice in the distribution of federal patronage. The breach between the two standard bearers—one heading the New Deal and a federal bureaucracy tremendously swollen by a swarm of new alphabetical agencies, the other all but worshiped as archangel of Share-Our-Wealth—widened from month to month. Roosevelt left the anti-Long philippics to members of his cabinet and other department heads: Hugh Johnson, NRA administrator, for example, or Interior Secretary Harold Ickes. The climax to these interchanges came in the late summer of 1935, when in an address delivered on the Senate floor, Long charged that “Franklin Delano Roosevelt the first, the last, and the littlest” was linked to a plot against his—Huey Long’s—life.
- 43. 3 —— August 8, 1935: Washington “I haven’t the slightest doubt but that Roosevelt would pardon anyone who killed Long.” ——UNIDENTIFIED VOICE FROM A DICTOGRAPH RECORD QUOTED BY HUEY LONG IN AN ADDRESS BEFORE THE UNITED STATES SENATE Long’s charge that he had been selected for assassination by a cabal in whose plot President Roosevelt was involved at least by implication made headlines from coast to coast and filled page on page of the Congressional Record. But it fell quite flat, being taken in a Pickwickian rather than in any literal sense. Even the unthinking elders of the Share-Our-Wealth clubs, their numbers now sadly shrunken by reason of the march of time, still cling to a rather pathetic belief in this extravagant bombast only by reason of an uncanny and unrelated coincidence: within less than thirty days after making the charge Long actually was assassinated. His climactic thrust at the White House was not taken too seriously at the time, however, because, for one thing, Long had cried “plot against me” too often. By the fall of 1935 the story was old hat, even though it had never before been blazoned in so august a tribunal as the Senate, and had never before involved, even by indirection, a chief executive. On two previous occasions he had placed Baton Rouge under martial law, calling out the militia, to defend him against plots on his life. Only seven months before making the Senate speech in question he had “exposed” the plot of
- 44. a group of Baton Rouge citizens, a number of high officials among them, to waylay his automobile on a given night while he was being driven to New Orleans, and kill him at a lonely bend of the River Road where the car would of necessity have to slow down. In proof of this he put on the witness stand an informer who had infiltrated into the ranks of the supposedly plotting group, and who testified as to the details of a conspiracy. Early in his senatorial career he had made himself so offensive in the washroom of a club at Sands Point, Long Island, that the irate victim of a demand to “make way for the Kingfish” slugged him. Since the blow split the skin over an eyebrow, the incident could not be concealed. Long promptly charged that hired bravos of the House of Morgan had assaulted him in the club washroom, intent on taking his life. Finally, when what he told the Senate on that August day in 1935 was boiled down in its own juices it made pretty thin gruel, as anyone who cares to wade through the fine print of the Congressional Record for that date can see for himself. The truth is that on the eve of Congress’ adjournment, Long was trying to build up against Roosevelt something he could tub-thump before the voters in the next year’s presidential campaign. On the principle that “the best defense is an attack,” he was keeping the New Deal hierarchy in Washington so busily occupied on another front that he could take advantage of their preoccupation to infiltrate Louisiana’s federal patronage with his followers. Presumably control over these appointments to all sorts of oddball positions under the PWA, WPA, and other auspices was now in the hands of the anti-Long contingent, headed by among others a good half of the state’s members in the lower house of Congress. But these were parochial politicians, fumblingly inept at organizing such matters on a state-wide scale. To cite but a single example, one project sponsored under the anti-Long dispensation was a review of the newspaper files in the New Orleans City Hall archives. By direction of Mayor Walmsley, so many appointees were packed into this particular task that they had to work in one-hour-a-day shifts in
- 45. order to find physical room in the small garret-like space set aside for it. Theoretically, they were to index these files, and to repair torn pages with gummed tape as they came across them. Actually, they would for the most part merely turn the leaves of the clumsy bound volumes until they came to the Sunday comics or other such features, and read these at leisure. Then they repaired to Lafayette Square when their hour of demanded presence was up, and joked about the way they would put out of joint the noses of the anti-Long leadership on election day; for of course most of them were dedicated Share-Our-Wealthers eagerly looking forward to $5000-a- year incomes when Huey Long got around to redistributing the nation’s wealth. Meanwhile their Kingfish was giving the anti-Long leaders a real Roland—an entire battalion of Rolands, in fact—for their patronage Oliver. The spoils-system theory of a patronage plum is that its bestowal is good for three votes; in other words, that the recipient and at least two members of his family or circle of friends will vote for the party favored by the job’s bestower. A United States senator would normally be consulted about appointments to all federal patronage posts not covered by civil service in his state: Collector of the Port, Surveyor of the Port, Collector of Internal Revenue, district attorneys, federal judges, and the like. During the early New Deal era this roster was tremendously amplified by the staffs of numerous new alphabetical agencies and their labor force. Huey Long may not have expected to be taken quite so literally when he told the Roosevelt hierarchs they could take their patronage “slap-dab to hell” as far as he was concerned. But when he saw that he was indeed given no voice in any Louisiana federal appointment, he initiated an entire series of special sessions of the state legislature which subserviently enacted a succession of so-called “dictatorship laws.” Under these statutes he took the control of every parochial and municipal position in every city, village, and parish out of the hands of the local authorities, and vested the appointive power in himself.
- 46. He did this by creating new state boards, composed of officials of his own selection, without whose certification no local public employee could receive or hold any post on the public payroll. A board of teacher certification was thus set up and without its—which is to say, Huey Long’s—approval, no teacher, janitor, school-bus driver, or principal could be employed by any local parish or city school board. No municipal police officer or deputy sheriff throughout the state, no deputy clerk or stenographer in any courthouse, no city or parish sanitary inspector, and so on down the entire line of public payroll places, could continue in his or her position unless specifically okayed by Senator Long. In those pre- civil-service days the appointive state, parish, and city employees in Louisiana outnumbered the federal patronage places within the state by hundreds to one, even during the New Deal’s era of production controls and “recovery.” Hence, for each federal patronage job he had nominally lost to his opponents he gained hundreds—literally—of local appointments which were thenceforth at his disposal. When this was pointed out in the anti-Long press and he was asked for comment, he chuckled and said: “I’m always ready to give anybody a biscuit for a barrel of flour.” In sum, he had brought practically all local public employees, including those who staffed Mayor Walmsley’s city administration in New Orleans, under the Long banner by the summer of 1935. Only a scant handful of “dictatorship laws” yet remained to be enacted, and these were already being drafted to his specifications. The moment Congress adjourned, when he would be released from Washington and could return to Louisiana, they would be rushed to enactment. Meanwhile he readied his parting shot against the White House. The incident on which he based the grotesque charge that President Roosevelt abetted, or at the very least knew of and acquiesced in, an assassination plot was a supposedly sub rosa political caucus held at the Hotel De Soto in New Orleans on Sunday, July 21, 1935. The gathering had been convened presumably without letting any outsider (i.e., “nonplotter”) know it was to be held. Its ostensible objective was the selection of an anti-Long gubernatorial candidate
- 47. whom all anti-Long factions would agree to support against any nominee the Senator might hand-pick for endorsement. However, with what still appears to be a positive genius for fumbling, the anti-Long leadership guarded with such butter- fingered zeal the secret of whether, where, or when they were to meet that even before they assembled, Long aides had ample time to install the microphone of a dictograph in the room where the anti- Long General Staff was to confer. The device functioned very fuzzily. Its recording (which it was hoped to duplicate and replay from sound trucks throughout the ensuing campaign) was only spottily intelligible. But a couple of court reporters had also been equipped with earphones at a listening post, and their stenographic transcript, though incomplete, afforded some excerpts which Senator Long inflated into what he presented as a full-scale murder plot. His fulmination was delivered before a crowded gallery, as usual. This popularity annoyed many of his senior colleagues, none more so than Vice-President Garner, whom John L. Lewis was soon to stigmatize as “that labor-baiting, poker-playing, whiskey-drinking evil old man.” More than once, as the galleries emptied with a rush the moment Long finished, Mr. Garner would call to the departing auditors, saying: “Yes, you can go now! The show’s over!” In this instance, as on many previous occasions, there was no advance hint of the fireworks to come. The fuse was a debate over the Frazier-Lemke bill, and Senator Long contented himself at the outset with charging that the administration was conducting “government by blackmail.” In making this statement he was referring to NIRA, which had succeeded NRA, the latter having been declared unconstitutional some three months earlier. This had nothing to do with the Frazier-Lemke bill, but it gave Mr. Long an opportunity to charge that no contracts for PWA work were being financed unless the contractor agreed to abide by all the provisions of the NRA code which the Supreme Court had invalidated. That led to the statement that “we in Louisiana have never stood for [such] blackmail from anybody,” which in turn led to a section of his arraignment the Congressional Record headed:
- 48. “THE PLAN OF ROBBERY, MURDER, BLACKMAIL, OR THEFT” He then loosed his farewell salvo. “I have a record of an anti-Long conference held by the anti-Long Representatives from Louisiana in Congress,” he said in part. “The faithful Roosevelt Congressmen had gone down there to put the Long crowd out.... Here is what happened among the Congressmen representing Roosevelt the first, the last and the littlest.” Holding aloft what he said was a transcript of the dictograph record, he listed the names of those present, naming a collector of internal revenue, an FERA manager for the state, and giving as the first direct quote of one of the conferees a statement made by one Oscar Whilden, a burly horse-and-mule dealer who had headed an anti-Long direct-action group calling itself the Square Deal Association. Whilden was quoted as saying at the very opening of the meeting that “I am out to murder, kill, bulldoze, steal or anything else to win this election!” An unidentified voice mentioned that the anti-Long faction would be aided by more “income tax indictments, and there will be some more convictions. They tell me O. K. Allen will be the next to be indicted.” “That,” explained Mr. Long for the benefit of his hearers and the press gallery, “is the governor of Louisiana. Send them down these culprits and thieves and thugs who openly advocate murdering people, and who have been participants in the murder of some people and in their undertaking to murder others—send them down these thugs and thieves and culprits and rascals who have been placed upon Government payrolls, drawing from five to six thousand dollars a year, to carry on and wage war in the name of the sacred flag, the Stars and Stripes. That is the kind of government to which the administration has attached itself in the state of Louisiana!” Four of Louisiana’s congressmen were named as having taken part in the caucus which Senator Long dubbed a “murder conference.” They were J. Y. Sanders, Jr., Cleveland Dear, Numa Montet, and John Sandlin. But it was another of the conferees whom Senator Long
- 49. quoted next, reading from the transcript, as suggesting that “we have Dear to make a trip around the state and then announce that the people want him to run for Governor, and no one will know about this arrangement here ... as you all know we must all keep all of this a secret and not even tell our own families of what is done.” Whereupon, according to the record, another voice proposed that “we should make fellows like Farley and Roosevelt and the suffering corporations ... cough up enough to get rid of that fellow.” Commented Senator Long: “Yes, we should make the Standard Oil Company and the ‘suffering corporations’ cough up enough ... says Mr. Sandlin ... [but] I am going to teach my friends in the Senate how to lick this kind of corruption. I am going to show them how to lick it to a shirttail finish.... I am going to give you a lesson in January to show you that the crookedness and rottenness and corruption of this Government, however ably [sic!] financed and however many big corporations join in it, will not get to first base.” More of the same sort of dialogue was read from the transcript. Congressman Sandlin assured the meeting that President Roosevelt will “endorse our candidate.” Another of the conferees, one O’Rourke, was described by Long as having refused to testify when another witness at an inquiry into one of Huey Long’s earlier murder- plot charges “swore that he had hired O’Rourke to commit murder in Baton Rouge. I was the man he was to kill so there was not much said about it except that he refused to testify on the ground that he would incriminate himself, whereupon Roosevelt employed him. He was qualified and he was appointed.” The statement most frequently quoted in the weeks and months that followed was that of an unidentified voice which the transcript reported as saying: “I would draw in a lottery to go out and kill Long. It would take only one man, one gun and one bullet.” And some time thereafter, according to the transcript, another unidentified voice declared that “I haven’t the slightest doubt but that Roosevelt would pardon any one who killed Long.” Thereupon someone asked: “But how could it be done?” and the reply was: “The best way would be to just hang around Washington and kill him right in the Senate.”
- 50. The conference was adjourned after notifying Congressman Dear that the people would clamor to have him run for governor of Louisiana. (The significance of this is that in one of Dear’s final campaign speeches he made the statement that gave rise to a widely disseminated and still persistent version of the shooting that followed, by almost exactly one month, the delivery of Long’s attack on the New Deal.) Long concluded his address to the Senate with the assertion that he had exposed this presumably hush-hush meeting “to the United States Senate and, I hope, to the country ... and I wish to announce further they have sent additional inspectors and various other bureaucrats down in the State.... “The State of Louisiana has no fear whatever of any kind of tactics thus agreed upon and thus imposed. The State of Louisiana will remain a state. When you hear from the election returns in the coming January ... Louisiana will not have a government imposed on it that represents murder, blackmail, oppression or destitution.” The Senate then resumed the business of the day. But most of the correspondents in the press gallery had left and the talk was all of Huey Long’s excoriation of the New Deal, of his promise that “if it is in a Presidential primary, they will hear from the people of the United States,” and of his declaration that rumors of the New Deal leaders plotting to have him murdered were now “fully verified.” Note: Most of the purely local references, repetitions, adversions to extraneous matters, and the like have been omitted from the foregoing condensation of Senator Long’s last speech before the Senate. Those who may wish to read the full text of his address will find it in the Congressional Record for August 9, 1935, pages 12780 through 12791. The section headed “The Plan of Robbery, Murder, Blackmail, or Theft” begins on page 12786, second column.
- 51. 4 —— August 30 to September 2 “Behold, my desire is that mine adversary had written a book. Surely I would take it upon my shoulder and bind it as a crown to me.” ——JOB Congress did not adjourn its 1935 session until seventeen days after Senator Long had delivered his blast about “the plan of robbery, murder, blackmail, or theft” at the Roosevelt administration in general and at its head in particular. This was, as he clearly stated in his reference to presidential primaries, the opening move in launching his 1936 candidacy for president; the next step would be publication and distribution of My First Days in the White House. He devoted himself to revision of this manuscript during the fortnight in which Congress remained in session, and marveled at the difficulties he encountered. Like many another magnetic orator, he was no writer, and in spite of the ghosts who had helped bring it into being, My First Days in the White House eloquently testifies to that fact. None the less, had he lived, the book would have won him adherents by the million. In all its naïve oversimplification, it was still a triumph of classical composition beside the helter-skelter phraseology of his senatorial and stump-speaking oratory. But the latter, like his many other public utterances, his early political circulars, and even the jumbled prose of his first book: Every Man a King, had been accepted almost as gospel by Longolators who
- 52. jeered at literate anti-Long editorials as propaganda dictated and paid for by the Money Barons. Congress did adjourn in due course, and now it is time to follow Long almost hour by hour through the final ten days of his life, assembling an unbiased chronicle in order to dispel myths and reveal truths about his assassination. His first concern was the publication of his book. His only other fixed commitment before having Governor Allen call the legislature into special session for the enactment of a final dossier of dictatorship laws, was delivery of a Labor Day address at Oklahoma City on September 2. He had accepted this invitation gladly, since it would afford him an opportunity to couple evangelistic grandiloquence about wealth- sharing with kind words about blind Senator Thomas Gore, who faced stiff opposition in his campaign for re-election. Earle Christenberry was left in charge of the Washington office, where he was to pack for transportation all documents and records which might be needed to elect a Long-endorsed governor and other state officials in Louisiana. Meanwhile, Mr. Long with the manuscript of his book and three of his bodyguards went to New York for a few days of relaxation. It was also part of his long-range design to seek the Democratic Party’s nomination for president at the 1936 convention. To be sure, he was under no misconception as to the sort of fate this bid would encounter. For one thing, Roosevelt’s personal popularity had reached new heights as his first term drew to a close. His nomination for a second term was all but inevitable. Long had attacked not only the administration as such. He was carrying on corrosive personal feuds with Postmaster General Farley, Interior Secretary Ickes, NRA Administrator Hugh Johnson, Senate Majority Leader Joe Robinson, and a host of other party bigwigs. Naturally, Louisiana’s Kingfish realized fully that these leaders, controlling the party machinery in the convention of 1936, would see to it not merely that F.D.R. received a virtually unanimous nomination for a second term, but that even were Roosevelt eliminated from contention, Huey Long’s effort to become the party’s standard bearer would be rejected.
- 53. Unquestionably, that is exactly what the Kingfish wanted. He already had a virtually crackproof national organization in his swiftly expanding Share-Our-Wealth clubs. The growth of this movement was now so rapid that his staff found difficulty in keeping pace with it. So valuable had its name become that both “Share Our Wealth” and “Share the Wealth” were copyrighted in Earle Christenberry’s name. Long’s purpose was to rally from both the Republican and Democratic camps the many who were still embittered by their struggles to escape the Great Depression. Times had undeniably bettered. The economy would reach a peak figure in 1937. But even the WPA “shovel leaners” were convinced that the government owed them much more than was being doled out on payday, and were entranced by the vision of a future in which Huey Long would soak the rich to provide for each toiler, however lowly his station, an income of $5000 a year and a span of mules. In the prairie corn and wheat belts, in the Dakotas and in Oklahoma, in all the places where Long had preached wealth-sharing while campaigning for Roosevelt, desperate landowners on the verge of eviction from mortgaged or tax-delinquent acres their forebears had carved out of the wilderness, were still rallying their friends and neighbors to help keep potential bidders from foreclosure auctions. These too would recall Long’s clamorous efforts to bring the Frazier- Lemke bill to a vote, and the conservatives’ success in holding it back from the floor. One and all, they would read My First Days in the White House, and they would learn in its pages how readily a wealth-sharing miracle could come to pass if only Huey Long were president.... None the less, publishers were chary of bringing out the book under their imprint. To Long this was no matter for concern. Over a period of at least three years a war chest for the presidential campaign he planned to wage in 1936 had been growing steadily. It included not merely money—a levy on the salaries of all public employees under his domination in Louisiana, and major campaign contributions from corporations that felt themselves obligated to show tangible appreciation for past favors or sought to insure
- 54. themselves against future reprisal—it included also a solid stockpile of affidavits about the boondoggles of divers federal agencies. Hard- pressed men, driven to almost any lengths by the crying need of their families for such bare necessities as food and shelter, were being forced to promise they would “praise Roosevelt and cuss Long” before being granted a WPA laborer’s pittance. At the outset of Long’s senatorial career this entire trove of cash and documentary dynamite was kept in some strongboxes of the Mayflower Hotel, where the Senator first established his capitol residence. But for various reasons, at least one of which was the hotel’s refusal to bar his political opponents from registering there while in Washington, his relations with the Mayflower deteriorated rapidly to the point where he moved to the Broadmoor, at 3601 Connecticut Avenue. The view from one of the windows of his apartment overlooking Rock Creek Park charmed him. At the same time the campaign cash and documents were transferred to the safety-deposit vaults of the Riggs National Bank, where the Senator kept a Washington checking account, or rather, where Earle Christenberry kept it for him. Hence the question of paying for the publication of My First Days in the White House presented no problem. For that matter, neither did the seeming permanence of a few scattered centers of anti-Long resistance in Louisiana. Since the dictatorship laws enacted during the previous twelvemonth made it virtually impossible to defeat Long proposals in the legislature, or Long candidates at the polls, the fixity of a few isolated opposition enclaves was desirable because, to quote Mr. Long, “it gives me somebody to cuss out, and I can’t make a speech that’s worth a damn unless I’m raising hell about what my enemies are doing.” Only one stubborn stronghold of this sort really irked him by its refusal to capitulate. This was the parish of St. Landry, whose seat was Opelousas. Always independent of alien dictation, this fourth- largest county in Louisiana had remained uncompromisingly anti- Long under the leadership of a couple of patriarchal autocrats: Judge Benjamin Pavy, tall, heavy-set, and wide-shouldered, with a roundish countenance against whose rather sallow complexion a
- 55. white mustache stood out in sharp contrast; and District Attorney Lee Garland, short and plump, his features pink beneath a flowing crest of white hair. Garland, much the elder, had held office continuously for forty-four years, Judge Pavy for twenty-eight. The latter had been elected to the district bench in 1908, after an exceptionally bitter local contest in which the leader of the anti-Pavy forces, Sheriff Marion Swords, went so far as to charge that one of Ben Pavy’s distant relatives-in- law was an individual the purity of whose Caucasian ancestry was open to challenge. Since Judge Pavy was elected not only then, but continuously thereafter for the next twenty-eight years in election after election, it is obvious the report was given no credence at the time. With the passage of years, the incident was forgotten. The situation in the parish of St. Landry would not have disturbed Huey Long too greatly, had there not been the possibility that in some future state Supreme Court election the heavy vote of that parish might upset the high tribunal’s political four-to-three Long- faction majority. On this ground alone it might be important for the Kingfish to alter the political climate of the St. Landry judicial district before the larger demands of an approaching presidential campaign monopolized his time and energy. A matter of prestige was likewise involved. It was Long’s purpose to take the stump personally in the St. Landry area, in order to bring about the defeat of its heavily entrenched Pavy-Garland faction and score a personal triumph. On the other hand, if through some mischance his persuasive oratory and the well-drilled efficiency of his cohorts failed to carry the day, the result would be hailed not merely in Louisiana, but throughout the nation, as a personal defeat for the Kingfish. Hence, nothing must be left to chance. Matters must be so arranged that failure was to all intents and purposes impossible. This involved no very serious difficulties. Earlier that summer, when he first outlined to his lieutenants plans for liquidating the Pavy-Garland entente as a politically potent factor, he gave orders to prepare for a special session of the legislature, this one to be called as soon as Congress adjourned. Once convened, the lawmakers were to gerrymander St. Landry from the thirteenth into the
- 56. fifteenth judicial district. This would leave Evangeline (Dr. Vidrine’s home bailiwick), small but overwhelmingly pro-Long, as the only parish in the thirteenth district, thus assuring the election of a friendly judge there. At the same time, it would annex St. Landry to another district which already included three large pro-Long parishes. Admittedly, the enlarged district would be given two judges instead of one, but under the new arrangement neither could possibly be elected without Long’s endorsement. Senator Long took it for granted that his wishes—commands, rather—would be complied with at once. But some close friends earnestly urged him to forgo the gerrymander, at least temporarily. Political feeling was running too high as matters stood to risk possible violence, perhaps even a popular uprising, through such high-handed and summary procedures. Reluctantly, he agreed to hold this particular project in abeyance, but only for the moment. At the close of August, however, with Congress in adjournment, and in view of the need to neutralize the federal government’s policy of patronage distribution solely for the benefit of his political foes back home, he decided that the time for action was at hand. Once more he sent word to Baton Rouge that preparations for a special legislative session, the fourth of that calendar year, be started without further delay. It should be convened on the night of Saturday, September 7. Meanwhile certain bills, embodying the statutory changes he wanted, should be drafted forthwith by Executive Counsel George Wallace, so that he—Huey—could check their wording in advance, and make any amendments he deemed necessary. This must be done with secrecy—not the sort of puerile intrigue with which his opponents had assembled their hotel conference, but under a tight cloak of concealment, so as to catch the opposition unawares. The gerrymander that would retire Judge Pavy to private life was to be the first measure introduced and passed, becoming House Bill Number One and later Act Number One. The date of the state’s congressional primaries was also to be moved up from September 1936 to January. These should be held at the same time as the
- 57. primaries for governor and other elective state officers. And there was another measure, one still in the planning stage, the details of which he would give later; something to take the sting out of Roosevelt’s punitive dispensation of federal patronage in Louisiana. Having disposed of these matters, Long left Washington for New York with three of his most trusted bodyguards—Murphy Roden, Paul Voitier, and Theophile Landry. All he had in mind at the moment was a day or two of relaxation. August 30 was his birthday. He would be forty-two years old. This in itself called for some sort of celebration. Besides, in view of the busy weeks ahead—the Labor Day speech in Oklahoma on September 2, the special session of the legislature, the need to rush My First Days in the White House into print, the fall and winter campaign for state offices, the presidential campaign to follow —this might well be, for no one knew how long, his last opportunity for casual diversion. “We flew to New York from Washington,” Captain Landry recalls, “and went straight to the New Yorker Hotel, where they always put the Senator in a suite on the thirty-second floor. We got there on August 29. I remember that because the next day, a Friday, was his birthday, and Ralph Hitz, the owner of the hotel, sent up a big birthday cake. Lila Lee, a New Orleans girl who was vocalist for Nick Lucas’ band that was playing the New Yorker’s supper room, came up to the suite with the cake to sing Happy-birthday-dear-Huey. After the cake had been cut and we all had a taste of it, he gave the rest to Miss Lee. “About that time Lou Irwin came up to take us out to dinner. I think the Senator had talked to him on the phone about finding someone to publish his book, and that Lou had said this was out of his line, since he was a theatrical agent, but he would inquire around and see what could be done. Earle Christenberry wasn’t with us. He had remained in Washington to gather up all the things the Senator might need in Louisiana, papers and so on, and he was going to take his time driving home with them while we went on to Oklahoma City. “Anyway, Lou Irwin said he had just booked a show into some place uptown. I have forgotten the name of it; all I remember is it
- 58. was quite a ways uptown, and Lou told us they had just imported from France some chef that made the best onion soup in the world. “So we went there to eat, and we had hardly sat down when who should come over to our table but Phil Baker, the radio star. He said: ‘Senator, I want you to meet the two most beautiful girls in New York, my wife Peggy and her niece.’ I don’t remember the niece’s name, but she was a young girl that looked to be about eighteen, and she was very pretty. Baker was all excited, talking about having just signed a contract that very day with the Gulf Refining people to take over their radio show, the one Will Rogers, who got killed in a plane crash with Wiley Post up in Alaska a couple of weeks before that, used to do.” The name of the niece was Cleanthe Carr. Her father, Gene Carr, was one of the best-known cartoonists and comic-strip originators in the country. His work was widely syndicated. “The Senator got up to dance with Mrs. Baker,” the Landry account continues, “and she must have told him, while they were dancing, about this niece being an artist, because when they came back to the table he picked up a napkin and gave it to this girl, saying: ‘Young lady, I understand you’re quite a cartoonist. Let’s see you sketch me here on this napkin!’ Well, she made a perfect sketch of him, with his arms out and his hair flying, as though he were making a hell-fire speech. He thought the sketch was fine, but Phil Baker said we ought to see some of her serious work, and we all should come up to his apartment, where he had quite a few of the paintings she had done. “So we left. I don’t think Lou Irwin came with us. But anyway, after we had been quite a long while at the Baker apartment, Senator Long said the niece would have to do the pictures for his book that he had written about how he was already elected president and what he did in the White House to redistribute the wealth after he was inaugurated. By the time we got back to the hotel it was three o’clock in the morning. “The Senator went over to the newsstand to look at the headlines in the morning papers, and a gentleman who had been in the lobby when we came in got up and came over to me and asked if my
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