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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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: 1661-7207
• 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