Random walks on convergence groups

[摘要] 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 GGG acts on a compact metrizable space MMM with the convergence property, then we can provide G∪MG\cup MG∪M with a compact topology such that random walks on GGG converge almost surely to points in MMM. Furthermore, we prove that if GGG is finitely generated and the random walk has finite entropy and finite logarithmic moment with respect to the word metric, then MMM, with the corresponding hitting measure, can be seen as a model for the Poisson boundary of GGG.

[学科分类] 神经科学