Geodesic
Random walks on convergence groups
Aitor Azemar1
1University of Glasgow, UK
Groups, geometry, and dynamics, Tome 16 (2022) no. 2, pp. 581-612

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DOI

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 G acts on a compact metrizable space M with the convergence property, then we can provide G∪M with a compact topology such that random walks on G converge almost surely to points in M. Furthermore, we prove that if G is finitely generated and the random walk has finite entropy and finite logarithmic moment with respect to the word metric, then M, with the corresponding hitting measure, can be seen as a model for the Poisson boundary of G.
DOI : 10.4171/ggd/654
Classification : 37-XX, 51-XX
Mots-clés : Poisson boundary

Aitor Azemar  1

1 University of Glasgow, UK 
Aitor Azemar. Random walks on convergence groups. Groups, geometry, and dynamics, Tome 16 (2022) no. 2, pp. 581-612. doi: 10.4171/ggd/654
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     doi = {10.4171/ggd/654},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/654/}
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