Random walks and geometry: Proc. workshop. Vienna, 2001

Vadim A. Kaimanovich, Klaus Schmidt, Wolfgang Woess3110172372, 9783110172379

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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Table of contents :
Preface……Page 7
Table of contents……Page 9
Surveys and longer articles……Page 11
Some Markov chains on abelian groups withapplications……Page 13
Random walks and physical models on infinitegraphs: an introduction……Page 45
The Garden of Eden Theorem for cellularautomata and for symbolic dynamical systems……Page 82
Expander graphs, random matricesand quantum chaos……Page 118
The Ihara zeta function of infinite graphs, the KNSspectral measure and integrable maps……Page 151
Simplicité de spectres de Lyapounov et propriétéd’isolation spectrale pour une famille d’opérateursde transfert sur l’espace projectif……Page 191
An introduction to the StochasticLoewner Evolution……Page 271
A canonical form for automorphisms of totallydisconnected locally compact groups……Page 305
On the classification of invariant measures forhorosphere foliations on nilpotent covers ofnegatively curved manifolds……Page 329
Markov processes on vermiculated spaces……Page 347
Cactus trees and lower bounds on the spectralradius of vertex-transitive graphs……Page 359
Equilibrium measure, Poisson kernel and effectiveresistance on networks……Page 373
Internal diffusion limited aggregation on discretegroups of polynomial growth……Page 386
On the physical relevance of random walks:an example of random walks on a randomlyoriented lattice……Page 403
Random walks, entropy and hopfianity of freegroups……Page 423
Growth rates of small cancellation groups……Page 431
Recurrence properties of random walks on finitevolume homogeneous manifolds……Page 441
On the cohomology of foliations with amenablegroupoid……Page 454
Linear rate of escape and convergence in direction……Page 469
Remarks on harmonic functions on affine buildings……Page 483
Random walks, spectral radii, and Ramanujangraphs……Page 496
Cogrowth of arbitrary graphs……Page 511
Total variation lower bounds for finiteMarkov chains: Wilson’s lemma……Page 525