An approach to traces of random walks on the boundary of a hyperbolic group via reflected Dirichlet spaces

Mathieu, Pierre
Tokushige, Yuki

Publication date

June 2022

Language

English

Abstract

We show the existence of a trace process at infinity for random walks on hyperbolic groups of conformal dimension $<2$. To do so, we employ the theory of Dirichlet forms which connects the theory of symmetric Markov processes to functional analytic perspectives. We introduce a family of Besov spaces associated to random walks and prove that they are isomorphic to some of the Besov spaces constructed from the co-homology of the group studied in Bourdon-Pajot (2003). We also study the regularity of harmonic measures of random walks on hyperbolic groups using the potential theory associated to Dirichlet forms.Comment: 44 page

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An approach to traces of random walks on the boundary of a hyperbolic group via reflected Dirichlet spaces

Abstract

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An approach to traces of random walks on the boundary of a hyperbolic group via reflected Dirichlet spaces

Abstract

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