Bessel Processes
Basic notions of probability theory and stochastic analysis are explained using the Brownian motion and its functionals. The concepts of probability space and filtration are introduced, and the strong Markov property and the martingale property of Brownia
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Makoto Katori
Bessel Processes, Schramm– Loewner Evolution, and the Dyson Model 123
SpringerBriefs in Mathematical Physics Volume 11
Series editors Nathanaël Berestycki, Cambridge, UK Mihalis Dafermos, Princeton, USA Tohru Eguchi, Tokyo, Japan Atsuo Kuniba, Tokyo, Japan Matilde Marcolli, Pasadena, USA Bruno Nachtergaele, Davis, USA
More information about this series at http://www.springer.com/series/11953
Makoto Katori
Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model
123
Makoto Katori Department of Physics Chuo University Tokyo Japan
Additional material to this book can be downloaded from http://extras.springer.com. ISSN 2197-1757 ISSN 2197-1765 (electronic) SpringerBriefs in Mathematical Physics ISBN 978-981-10-0274-8 ISBN 978-981-10-0275-5 (eBook) DOI 10.1007/978-981-10-0275-5 Library of Congress Control Number: 2015959919 © The Author(s) 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 This Springer imprint is published by SpringerNature The registered company is Springer Science+Business Media Singapore Pte Ltd.
To Hiroko, Machiko, and Rieko
Preface
This book is based on my graduate-course lectures given at the Graduate School of Mathematics of the University of Tokyo in October 2008 (at the invitation of T. Funaki and M. Jimbo), at the Department of Physics of the University of Tokyo in November 2010 (at the invitation of S. Miyashita), at the Department of Mathematics of Tokyo Institute of Technology in December 2010 (at the invitation of K. Uchiyama), at École de Physique des Houches (Les Houches Physics School) in May 2011 (organized by C. Donati-Martin, S. Péché and G. Schehr), at the Faculty of Mathematics of Kyushu University in June 2013 (at the invitation of H. Osada and T. Shirai), and at the Graduate School of Arts and Sciences of the University of Tokyo in July 2014 (at the invitation of A. Shimizu). First of all I would like to thank those organizers for giving me such opportunities. The purpose o
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