The ratio set of the harmonic measure of a random walk on a hyperbolic group

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We consider the harmonic measure on the Gromov boundary of a nonamenable hyperbolic group defined by a finite range random walk on the group, and study the corresponding orbit equivalence relation on the boundary. It is known to be always amenable and of type III. We determine its ratio set by showing that it is generated by certain values of the Martin kernel. In particular, we show that the equivalence relation is never of type III_0.
21 pages

Keywords

Dynamical Systems, Group Theory, Operator Algebras, Probability

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/109026

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0602409
 http://arxiv.org/abs/math/0602409

Collections

arXiv