Andrei Alpeev

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math.DS2025

A characterization of $C^{*}$ -simplicity of countable groups via Poisson boundaries

Andrei Alpeev

We characterize $C^{*}$ -simplicity for countable groups by means of the following dichotomy. If a group is $C^{*}$ -simple, then the action on the Poisson boundary is essentially free f…

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…

A characterization of C∗-simplicity of countable groups via Poisson boundaries

Secret sharing on the Poisson-Furstenberg boundary I

A characterization of $C^{*}$ -simplicity of countable groups via Poisson boundaries