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 G acts on a compact metrizable space M with the convergence property, then we can provide G\cup 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 .
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