Boundaries for random walks on hyperbolic groups
by
Chris Connell
Indiana University (currently at MSRI)
Coauthors: Roman Muchnik

This is the last of three talks by Roman Muchnik and myself. I will present work in progress on the existence of stationary measures for generalized Gibbs states. The usual Gibbs states are a family of measures which includes essentially every interesting measure on the geodesic boundary of a CAT(-1) space. We show that for a large class of hyperbolic groups and Gibbs states one can explicitly construct random walks on the group such that the Gibbs state and its support are a Poisson boundary. We will also consider applications.

Date received: January 6, 2004