Mathematical Methods for Hydrodynamic Limits
Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a va
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Anna De Masi
Errico Presutti
Mathematical Methods for Hydrodynamic Limits
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Authors Anna De Masi Dipartimento di Matematica Pura ed Applicata Universita di L'Aquila 67100 L' Aquila, Italy Errico Presutti Dipartimento di Matematica Universita di Roma Tor Vergata Via Fontanile di Carcaricola 00133 Roma, Italy
Mathematics Subject Classification (1991): 60-02, 60K35, 82A05
ISBN 3-540-55004-6 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-55004-6 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this 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 1991 Printed in Germany Typesetting: Camera ready by author Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 46/3140-543210 - Printed on acid-free paper
To the memory of our friend Piero de Mottoni
Preface
The idea of writing tbis book came after a course given in Boulder, Colorado, in 1988, by one of us, (E.P.). At tbat time tbe paper of Guo, Papanicolaou and Varadban bad just appeared. Dave vVick, wbo bad worked bimself on entropy inequalities in interacting particle systems and was in Boulder at tbe same time, was very interested on these new results and we tried together to understand tbem. We were very much helped by tbe interest and participation of Dick Holley. This was the starting point, then tbe discussion went on, covering other methods used for studying the bydrodynamic behavior of interacting particle systems. In the end, we thought it wortbwbile to save the material as an introductory course on the collective phenomena in particle systems. Unfortunately Dave did not want to take part to this last effort, and the task of actually writing down some notes was left to the present authors. vVe used the notes in seminars and short courses, as well as in a School organized' by Rolando Rebolledo in Santiago of Chile. The result was not what we were hoping for: too many details missing, at least for younger researchers without a solid background in probability and/or statistical mechanics. We therefore tried to add new topics, we made a preprint, [42J, and waited for reactions. iVe have been lud:y, many colleagues had tbe patience of reading our preprint and to suggest improvements. iVe are also very grateful to several students in L'Aquila and the University of Roma "La Sapienza" who read our work trying to understand it, they have been most helpful in rewriting the present version, which, i
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