Random Walks and Geometry: Proceedings of a Workshop at the Erwin Schrödinger Institute, Vienna, June 18-July 13, 2001

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Vadim A. Kaimanovich, Klaus Schmidt, Wolfgang Woess
Walter de Gruyter, 2004 - Science - 532 pages

Recent developments show that probability methods have become a very powerful tool in such different areas as statistical physics, dynamical systems, Riemannian geometry, group theory, harmonic analysis, graph theory and computer science.

This volume is an outcome of the special semester 2001 - Random Walks held at the Schrödinger Institute in Vienna, Austria. It contains original research articles with non-trivial new approaches based on applications of random walks and similar processes to Lie groups, geometric flows, physical models on infinite graphs, random number generators, Lyapunov exponents, geometric group theory, spectral theory of graphs and potential theory. Highlights are the first survey of the theory of the stochastic Loewner evolution and its applications to percolation theory (a new rapidly developing and very promising subject at the crossroads of probability, statistical physics and harmonic analysis), surveys on expander graphs, random matrices and quantum chaos, cellular automata and symbolic dynamical systems, and others.

The contributors to the volume are the leading experts in the area. The book will provide a valuable source both for active researchers and graduate students in the respective fields.

 

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Contents

Raffaella Burioni Davide Cassi and Alessandro Vezzani
36
Random walks
42
Harmonic oscillations
55
Introduction
61
Tullio CeccheriniSilberstein Francesca Fiorenzi and Fabio Scarabotti
73
Alex Gamburd
109
Grigorchuk and Andrzej Zuk
141
Yves Guivarch et Émile Le Page
181
Enrique Bendito Ángeles Carmona and Andrés M Encinas
363
Sébastien Blachère
377
Massimo Campanino and Dimitri Petritis
393
Tullio CeccheriniSilberstein and Fabio Scarabotti
413
Alex Eskin and Gregory Margulis
431
Alessandra Iozzi
445
Anders Karlsson
459
Anna Maria Mantero and Anna Zappa
473

Gregory F Lawler
261
George A Willis
295
Martine Babillot
319
Martin T Barlow and Steven N Evans
337
Laurent Bartholdi
349
Tatiana Nagnibeda
487
Sam Northshield
501
Laurent SaloffCoste
515
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