Scaling Limits of Interacting Particle Systems
The idea of writing up a book on the hydrodynamic behavior of interacting particle systems was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the spring of 1988. At this time Claude wrote some notes in French that cover
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Editors
S. S. Chern B. Eckmann P. de Ia Harpe H. Hironaka F. Hirzebruch N. Hitchin L. Hörmander M.-A. Knus A. Kupiainen J. Lannes G. Lebeau M. Ratner D. Serre Ya.G. Sinai N. J. A. Sloane J.Tits M. Waldschmidt S. Watanabe Managing Editors
M. Berger J. Coates S. R. S. Varadhan
320
Springer-Verlag Berlin Heidelberg GmbH
Claude Kipnis Claudio Landim
Scaling Limits of Interacting Particle Systems
Springer
Claude Kipnist Claudio Landim Instituto de Matematica Pura e Aplicada Estrada Dona Castorina 110 22460-320 Rio de Janeiro, Brasil
and CNRS UPRES-A 6085 Universite de Rouen F-76128 Mont Saint Aignan Cedex, France
Library of Congress Cataloging-in-Publication Data Kipnis, CI aude, 1949-1993 Scaling limits of interacting partide systems 1 Claude Kipnis, Claudio Landim. p. cm. - (Grundlehren der mathematischen Wissenschaften ; 320) Indudes bibliographical references and index. ISBN 978-3-662-03752-2 (eBook) ISBN 978-3-642-08444-7 DOI 10.1007/978-3-662-03752-2
Scaling laws (Statistic al physics) 2. Probabilities. 3. Markov processes. 4. Hydrodynamics--Mathematics. 5. Mathematical physics. 1. Landim, Claudio. II. Tide. III. Series. QC174.85.S34L36 1999 532' .5--dc21
1.
Mathematics Subject Classification (1991): 60-02, 60K35, 82A05
ISSN 0072-7830 ISBN 978-3-642-08444-7 This work is subject to copyright. AII rights are reserved, whether the whole or part ofthe material is concerned, specifically the rights oftranslation, reprinting, reuse of iIlustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication ofthis publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer- Verlag Berlin Heidelberg 1999 Originally published by Springer-Verlag Berlin Heidelberg New York in 1999 Softcover reprint of the hardcover lSt edition 1999
Cover design: MetaDesign plus GmbH, Berlin Typesetting by the author using a Springer TEX macro-package SPIN: 10631667 41/3143-5 4 3 21 o Printed on acid-free paper
A minha filha Anna Aos meus pais Raul e Regina
Preface
The idea of writing up a book on the hydrodynamic behavior of interacting particle systems was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the spring of 1988. At this time Claude wrote some notes in French that covered Chapters 1 and 4, parts of Chapters 2, 5 and Appendix 1 of this book. His intention was to prepare a text that was as self-contained as possible. lt would include, for instance, all tools from Markov process theory (cf. Appendix 1, Chaps. 2 and 4) necessary to enable mathematicians and mathematical physicists with some knowledge of probability, at the Ievel of Chung (1974), to understand the techniques of the theory of hydrodynamic Iimits of interacting particle systems. In the fall of 1991 Claude invited me to complete his n
