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 acts on a compact metrizable space with the convergence property, then we can provide with a compact topology such that random walks on converge almost surely to points in . Furthermore, we prove that if is finitely generated and the random walk has finite entropy and finite logarithmic moment with respect to the word metric, then , with the corresponding hitting measure, can be seen as a model for the Poisson boundary of .
Cite this article
Aitor Azemar, Random walks on convergence groups. Groups Geom. Dyn. 16 (2022), no. 2, pp. 581–612DOI 10.4171/GGD/654