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arXiv · 0802.2837

On amenability of automata groups

Laurent Bartholdi·Vadim A. Kaimanovich·Volodymyr V. Nekrashevych
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Abstract

We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The proof is based on reducing the problem to showing amenability just of a certain explicit family of groups ("Mother groups") which is done by analyzing the asymptotic properties of random walks on these groups.

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Laurent Bartholdi, Vadim A. Kaimanovich, Volodymyr V. Nekrashevych. 2008-02-20. On amenability of automata groups. https://doi.org/10.1215/00127094-2010-046

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