3 papers
math.DS2025
A characterization of -simplicity of countable groups via Poisson boundaries
Andrei Alpeev
We characterize -simplicity for countable groups by means of the following dichotomy. If a group is -simple, then the action on the Poisson boundary is essentially free f…
math.GR2024
Non-C*-simple groups admit non-free actions on their Poisson boundaries
Andrei Alpeev
It is a classical result of Kaimanovich and Vershik and independently of Rosenblatt that a non-amenable group admits a non-degenerate symmetric measure such that the Poisson bounda…
math.DS2024
Secret sharing on the Poisson-Furstenberg boundary I
Andrei Alpeev
Recently, Vadim Kaimanovich presented a particular example of a measure on a product of two standard lamplighter groups such that the Poisson boundary of the induced random walk is…