Choquet-Deny groups and the infinite conjugacy class property
Annals of Mathematics, pp. 307-320, 2019.
A countable discrete group $G$ is said to be Choquet-Deny if it has a trivial Poisson boundary for every generating probability measure. We show that a finitely generated group $G$ is Choquet-Deny if and only if it is virtually nilpotent. Moreover, when $G$ is not virtually nilpotent, then the Poisson boundary is non-trivial for a generat...更多