Brownian Motion, Obstacles and Random Media
This book is aimed at graduate students and researchers. It provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion and random obstacles. This subject has a rich phenomenolo
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Springer-Verlag Berlin Heidelberg GmbH
Alain -Sol Sznitman
Brownian Motion, Obstacles and Random Media With 45 Figures
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Springer
Alain-Sol Sznitman FIM ETH Zurich 8092 Zurich Switzerland
Libraryof Congress Cataloging-in-Publieation Data Sznitman, Alain-Sol. Brownian motion, obstacles and random media 1Alain-Sol Sznitman. p. em. -- (Springer monographs in mathematics) Includes bibliographical referenees and index. ISBN 978-3-642-08420-1 ISBN 978-3-662-11281-6 (eBook) DOI 10.1007/978-3-662-11281-6 1. Brownian
motion proeesses. 2. Random fields.1. Tide.
II. Series. QA274.75.S95 1998 530.4'75--de21
Mathematics Subject Classification (1991): 60K40, 60}45, 35P15,82D30
This work is subjeet to copyright. All rights are reserved, whether the whole ar part of the material is coneerned, specifieally the rights of translation, reprinting, reuse of illustrations, recitation, broadeasting, reproduction an microfilm ar 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 Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1998 Originally published by Springer-Verlag Berlin Heidelberg New York in 1998 Softcover reprint ofthe hardcover lst edition 1998
The use of general descriptive names, registered names, trademarks etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt [rom the relevant protective laws and regulations and therefore free for general use. Cover design: Erich Kirchner, Heidelberg Typesetting by the author using LateX SPIN 10660412 41/3143-543210 - Printedon acid-free paper
Preface
The principal purpose of this book is to provide an account of the circle of ideas, results and techniques, which emerged roughly over the last ten years in the study of Brownian motion and random obstacles. The accumulation of results in many separate sources eventually made it impractical, if not impossible, for the nonspecialist to gain access to the developments of the subject. This book is an attempt to remedy this situation. Part of the thrill of the investigation of Brownian motion and random obstacles certainly stems from its many connections with various areas of mathematics, but also from the formal and mysterious physical heuristics which relate to it. In particular the loose concept of pockets of low local eigenvalues plays an important role in the study of Brownian motion and random obstacles, and also represents a paradigm which has natural resonances with several other areas of random media. This last feature has increasingly become clear over the last few years. This book grew out of a series of graduate lectures at the ETH Ziirich, which took place between the Fall '93 and the Spring '97, and surveyed a selection of topics from the theory of random medi
