Metastability A Potential-Theoretic Approach
Metastability is a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise. This monograph provides a concise presentation o
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Anton Bovier Frank den Hollander
Metastability A Potential-Theoretic Approach
Grundlehren der mathematischen Wissenschaften A Series of Comprehensive Studies in Mathematics
Series editors M. Berger P. de la Harpe N.J. Hitchin A. Kupiainen G. Lebeau F.-H. Lin S. Mori B.C. Ngô M. Ratner D. Serre N.J.A. Sloane A.M. Vershik M. Waldschmidt Editor-in-Chief A. Chenciner J. Coates
S.R.S. Varadhan
351
For further volumes: www.springer.com/series/138
Anton Bovier r Frank den Hollander
Metastability A Potential-Theoretic Approach
Anton Bovier Institut für Angewandte Mathematik Rheinische Friedrich-Wilhelms-Universität Bonn, Germany
Frank den Hollander Mathematisch Instituut Universiteit Leiden Leiden, The Netherlands
ISSN 0072-7830 ISSN 2196-9701 (electronic) Grundlehren der mathematischen Wissenschaften ISBN 978-3-319-24775-5 ISBN 978-3-319-24777-9 (eBook) DOI 10.1007/978-3-319-24777-9 Library of Congress Control Number: 2015959720 Mathematics Subject Classification (2010): 60K35, 60J45, 82C26 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
C’est une grande folie de vouloir être sage tout seul. (François de La Rochefoucauld, Réflexions)
Metastability is a wide-spread phenomenon in the dynamics of non-linear systems— physical, chemical, biological or economic—subject to the action of temporal random forces typically referred to as noise. In the narrower perspective of statistical physics, metastable behaviour can be seen as the dynamical manifestation of a first-order phase transition, i.e., a crossover that involves a jump in some intrinsic physical parameter such as the energy density or the magnetisation. Attempts to understand and model metastable systems mathematically go back to the early 20th century, notably through the work of H. Eyring and H.A. Kramer
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