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Choquet-Deny groups and the infinite conjugacy class property. (arXiv:1802.00751v1 [math.GR])
来源于:arXiv
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 generating measure that is symmetric and has
finite entropy. For general countable discrete groups, we show that $G$ is
Choquet-Deny if and only if none of its quotients have the infinite conjugacy
class property. 查看全文>>