From Classical to Modern Probability CIMPA Summer School 2001
This volume is based on lectures notes for the courses delivered at the Cimpa Summer School: From Classical to Modern Probability, held at Temuco, Chile, be th th tween January 8 and 26 , 2001. This meeting brought together probabilists and graduate stud
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Series Editors Thomas Liggett Charles Newman Loren Pitt Sidney I. Resnick
From Classical to Modern Probability CIMPA Summer School 2001
Pierre Picco Jaime San Martin Editors
Springer Basel AG
Editors' addresses: Pierre Picco Centre de Physique Theorique CNRS Campus de Luminy Case 907 13288 Marseille Cedex 9 France e-mail: [email protected]
Jaime San Martin Departamento de Ingenieria Matematica Universidad de Chile Blanco Encalada 2120 Santiago Chile e-mail: [email protected]
2000 Mathematics Subject Classification 60-06; 31C15, 35K05, 60F05, 60FlO, 60J05, 60J65,82B26
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at . ISBN 978-3-0348-9422-7 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, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2003 Springer Base) AG Originally published by Birkhauser Verlag Basel in 2003 Softcover reprint ofthe hardcover Ist edition 2003 Printed on acid-free paper produced from chlorine-free pulp. TCF 00 ISBN 978-3-0348-9422-7 ISBN 978-3-0348-8053-4 (eBook) DOI 10.1007/978-3-0348-8053-4 987 65432 1 www.birkhasuer-science.com
Contents Foreword .................................................................
Vll
Introduction ..............................................................
IX
The game of Dudo ........................................................
xv
P. Collet Asymptotic of the Heat Kernel in Unbounded Domains 1 Introduction ......................................................... 2 Ratio theorem for domains with harmonic cone Cn of dimension 1 ... 3 Benedicks domains .................................................. References ................................................................
1 7 12 22
A. De Masi Spin Systems with Long Range Interactions 1 Ising spin systems ................................................... 2 Phase transition ..................................................... 3 Time evolution ...................................................... References ................................................................
26 43 56 78
C. Dellacherie Nonlinear Dirichlet Problem and Nonlinear Integration 1 Generalities ......................................................... 2 Preliminaries on capacities .......................................... 3 Radon capacities .................................................... 4 Lusin capacities ..................................................... 5 Answering the questions and last words .............................. References ............................................
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