Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory
Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduce
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w. BeiglbOck R.P.Geroch E.H.Lieb T.Regge W. Thirring Series Editors
Roberto Fernandez
JUrg Frohl ich AI an D. Sakal
Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory With 26 Figures
Springer-Verlag Berlin Heidelberg GmbH
Dr. Roberto Fernandez Professor Jiirg Frohlich Institut flir Theoretische Physik, ETH Hiinggerberg CH-8093 Zurich, Switzerland
Professor Alan D. Sokal Department of Physics, New York University 4, Washington Place, New York, NY 10003, USA
Editors Wolf Beiglbock
Tullio Regge
Institut flir Angewandte Mathematik Universitat Heidelberg 1m Neuenheimer Feld 294 W-6900 Heidelberg 1, FRO
Instituto di Fisica Teorica Universita di Torino, C. so M. d' Azeglio, 46 1-10125 Torino, Italy
Robert P. Geroch Enrico Fermi Institute University of Chicago 5640 Ellis Ave. Chicago, IL 60637, USA
Walter Thirring Institut flir Theoretische Physik der Universitat Wien Boltzmanngasse 5 A-I090 Wien, Austria
Elliott H. Lieb Jadwin Hall P. O. Box 708 Princeton University Princeton, NJ 08544-0708, USA
ISBN 978-3-662-02868-1 Library of Congress Cataloging-in-Publication Data. Fernandez, R. (Roberto), 1951-. Random Walks, critical phenomena, and triviality in quantum field theory / R. Fernandez, J. Frohlich, A. D. Sokal. p. cm. -- (Texts and monographs in physics). Includes bibliographical references and index. 1. Quantum
ISBN 978-3-662-02868-1 ISBN 978-3-662-02866-7 (eBook) DOI 10.1007/978-3-662-02866-7 field theory. 2. Random walks (Mathematics). 3. Critical phenomena (Physics). I. Frohlich, J. (JUrg.), 1946-. II. Sokal, A. D. (Alan D.), 1955-. III. Title. IV. Series. QCI74.45.F46 1991 530.1'43--dc20 91-40850 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other ways, 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 1992 Originally published by Springer-Verlag Berlin Heidelberg New York in 1992 Softcover reprint of the hardcover I Sl edition 1992 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 from the relevant protective laws and regulations and therefore free for general use.
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Foreword
Simple random walks - or equivalently, sums of independent random variables - have long been a standard topic of probability theory and mathematical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoidin
