Random walks on convergence groups

Azemar, A. (2022) Random walks on convergence groups. Groups, Geometry and Dynamics, 16(2), pp. 581-612. (doi: 10.4171/ggd/654)

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We extend some properties of random walks on hyperbolic groups to random walks on convergence groups. In particular, we prove that if a convergence group GG acts on a compact metrizable space MM with the convergence property, then we can provide G\cup MG∪M with a compact topology such that random walks on GG converge almost surely to points in MM. Furthermore, we prove that if GG is finitely generated and the random walk has finite entropy and finite logarithmic moment with respect to the word metric, then MM, with the corresponding hitting measure, can be seen as a model for the Poisson boundary of GG.

Item Type:Articles
Keywords:Discrete Mathematics and Combinatorics, Geometry and Topology
Glasgow Author(s) Enlighten ID:Azemar, Mr Aitor
Authors: Azemar, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Groups, Geometry and Dynamics
Publisher:European Mathematical Society
ISSN (Online):1661-7215
Published Online:24 September 2022
Copyright Holders:Copyright © 2022 European Mathematical Society
First Published:First published in Groups, Geometry and Dynamics 16(2): 581-612
Publisher Policy:Reproduced under a Creative Commons License

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