4 papers
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…
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…
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…
Krieger's finite generator theorem for actions of countable groups III
Andrei Alpeev, Brandon Seward
We continue the study of Rokhlin entropy, an isomorphism invariant for probability-measure-preserving actions of countable groups introduced in Part I. In this paper we prove a non…