The Poisson boundary of hyperbolic groups without moment conditions

Kunal Chawla; Behrang Forghani; Joshua Frisch; Giulio Tiozzo

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arXiv · 2209.02114

The Poisson boundary of hyperbolic groups without moment conditions

Kunal Chawla·Behrang Forghani·Joshua Frisch·Giulio Tiozzo

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Abstract

We prove that the Poisson boundary of a random walk with finite entropy on a non-elementary hyperbolic group can be identified with its hyperbolic boundary, without assuming any moment condition on the measure. We also extend our method to groups with an action by isometries on a hyperbolic metric space containing a WPD element; this applies to a large class of non-hyperbolic groups such as relatively hyperbolic groups, mapping class groups, and groups acting on CAT(0) spaces.

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BibTeX RIS

Kunal Chawla, Behrang Forghani, Joshua Frisch, Giulio Tiozzo. 2022-09-05. The Poisson boundary of hyperbolic groups without moment conditions. https://arxiv.org/abs/2209.02114

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