"münchhausen Trick" and Amenability of Self-similar Groups

Abstract

The structure of a self-similar group G naturally gives rise to a transformation which assigns to any probability measure μ on G and any word w in the alphabet of the group a new probability measure μ. If μ is a convex combination of μ and the δ-measure at the group identity, then the asymptotic entropy of the random walk (G,μ) vanishes; therefore, the random walk is Liouville and the group G is amenable. Using this method we prove amenability of several classes of self-similar groups.

DOI: 10.1142/S0218196705002694

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Cite this paper

@article{Kaimanovich2005mnchhausenTA, title={"m{\"{u}nchhausen Trick" and Amenability of Self-similar Groups}, author={Vadim A. Kaimanovich}, journal={IJAC}, year={2005}, volume={15}, pages={907-938} }