Random Walks and Geometry (eBook)

Proceedings of a Workshop at the Erwin Schrödinger Institute, Vienna, June 18 - July 13, 2001

Vadim Kaimanovich (Herausgeber)

eBook Download: PDF

2004
542 Seiten
De Gruyter (Verlag)
978-3-11-019808-9 (ISBN)

Infos

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.

Inhalt

Frontmatter 1
Table of contents 9
Some Markov chains on abelian groups with applications 13
Random walks and physical models on infinite graphs: an introduction 45
The Garden of Eden Theorem for cellular automata and for symbolic dynamical systems 83
Expander graphs, random matrices and quantum chaos 119
The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps 151
Simplicité de spectres de Lyapounov et propriété d’isolation spectrale pour une famille d’opérateurs de transfert sur l’espace projectif 191
An introduction to the Stochastic Loewner Evolution 271
A canonical form for automorphisms of totally disconnected locally compact groups 305
On the classification of invariant measures for horosphere foliations on nilpotent covers of negatively curved manifolds 329
Markov processes on vermiculated spaces 347
Cactus trees and lower bounds on the spectral radius of vertex-transitive graphs 359
Equilibrium measure, Poisson kernel and effective resistance on networks 373
Internal diffusion limited aggregation on discrete groups of polynomial growth 387
On the physical relevance of random walks: an example of random walks on a randomly oriented lattice 403
Random walks, entropy and hopfianity of free groups 423
Growth rates of small cancellation groups 431
Recurrence properties of random walks on finite volume homogeneous manifolds 441
On the cohomology of foliations with amenable groupoid 455
Linear rate of escape and convergence in direction 469
Remarks on harmonic functions on affine buildings 483
Random walks, spectral radii, and Ramanujan graphs 497
Cogrowth of arbitrary graphs 511
Total variation lower bounds for finite Markov chains: Wilson’s lemma 525
Backmatter 541

Produkt-Details

• Erscheint lt. Verlag: 22.8.2008
• Reihe/Serie: De Gruyter Proceedings in Mathematics
• Reihe/Serie: De Gruyter Proceedings in Mathematics
• Reihe/Serie: ISSN
• Co-Autor: Klaus Schmidt, Wolfgang Woess
• Verlagsort: Berlin/Boston
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Technik
• Schlagworte: Harmonische Funktion • Irrfahrt (Math.) • Markowscher Prozess • Quantenchaos • Spektraltheorie
• ISBN-10: 3-11-019808-8 / 3110198088
• ISBN-13: 978-3-11-019808-9 / 9783110198089