Appears in collection : 2022 - T2 - WS2 - Self-similarity of groups, trees and fractals

The Poisson boundary of a group is a probabilistic object which serves a dual role. It represents the space of asymptotic trajectories a random walk might take and it represents the possible space of bounded harmonic functions on a group.

In this talk I will discuss the Poisson boundary for linear groups. In particular I will focus on the question of when the boundary is trivial in which case all bounded harmonic functions on the group are constant. This is joint work with Anna Erschler.