Random Walks, Brownian Motion, and Interacting Particle Systems A Fe
This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on pr
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Series Editors Thomas Liggett Charles Newman Loren Pitt
Random Walks, Brownian Motion, and Interacting Particle Systems A Festschrift in Honor of Frank Spitzer
Rick Durrett Harry Kesten Editors
Springer Science+Business Media, LLC
Rick Durrett Department of Mathematics Cornell University White Hau Ithaca, NY 14853
Harry Kesten Department of Mathematics Cornell University White Hall Ithaca, NY 14853
Library of Congress cataloging-in-publication data Random walks, Brownian motion, and interacting particle systems / Rick Durrett, Harry Kesten, editors. p. cm. — (Progress in probability : v. 28) Festschrift in honor of Frank Spitzer. Includes bibliographical references and index. ISBN 978-1-4612-6770-6 ISBN 978-1-4612-0459-6 (eBook) DOI 10.1007/978-1-4612-0459-6 1. Random walks (Mathematics) 2. Brownian motion processes. 3. Probabilities. 4. Statistical physics. 5. Spitzer, Frank, 1926I. Durrett, Richard, 1951II. Kesten, Harry, 1931in. Spitzer, Frank, 1926- . IV. Series: Progress in probability : 28. QC174.85.R37R37 1991 91-31173 519.2-dc20 CIP Printed on acid-free paper. © Springer Science+Business Media New York 1991 Originally published by Birkhäuser Boston in 1991 Softcover reprint of the hardcover 1st edition 1991 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use of specific clients is granted by Springer Science+Business Media, L L C , for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $0.00 per copy, plus $0.20 per page is paid directly to CCC, 21 Congress Street, Salem, M A 01970, U.S.A. Special requests should be addressed directly to Springer Science+Business Media, L L C . ISBN 978-1-4612-6770-6 Typset by authors in TeX. 987654321
ABOUT THE COVER
The editors wish to thank Robert Fisch and David Griffeath for the graphic on the cover. The graphic depicts convergence to equilibrium in a system of particles which perform random walks under the "exclusion" restriction that there may be at most one particle per lattice site. Initially the particles are packed in a tight ball and successive "still frames" show the state of the system at times 10, 100, 1000 and 10000 (on a 256 x 256 lattice with wrap-around) . The picture was produced using the hardware and software of T. Toffoli and N. Margolus. A Matrix film recorder, funded by the National Science Foundation, made the transparency used in the printing process.
STUDENTS OF FRANK SPITZER 1957 J. W. Lamperti, On the asymptotic behavior of recurrent and almostrecurrent events. 1964 W. W. Whitman, Some strong laws for random walks and Brownian motion. 1965 J. C. Mineka, The existence and uniqueness of positive solutions to the Wiener-Hopf equation with positive kernel. 1969 R. A. Holley, The motion of a heavy particle in an infinite one-di
