Geometric criteria for the Poisson boundary of locally compact groups

Behrang Forghani, Giulio Tiozzo

Published 2018-12-18Version 1

We consider random walks on locally compact groups, extending the geometric criteria for the identification of their Poisson boundary previously known for discrete groups. First, we prove a version of the Shannon-McMillan-Breiman theorem, which we then use to generalize Kaimanovich's ray approximation and strip approximation criteria. We give several applications to identify the Poisson boundary of locally compact groups which act by isometries on nonpositively curved spaces.