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15 September 2010 On amenability of automata groups
Laurent Bartholdi, Vadim A. Kaimanovich, Volodymyr V. Nekrashevych
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Duke Math. J. 154(3): 575-598 (15 September 2010). DOI: 10.1215/00127094-2010-046

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. "On amenability of automata groups." Duke Math. J. 154 (3) 575 - 598, 15 September 2010. https://doi.org/10.1215/00127094-2010-046

Information

Published: 15 September 2010
First available in Project Euclid: 7 September 2010

zbMATH: 1185.37020
MathSciNet: MR2730578
Digital Object Identifier: 10.1215/00127094-2010-046

Subjects:
Primary: 20E08
Secondary: 20P05 , 37A50 , ‎43A07‎ , 60G50

Rights: Copyright © 2010 Duke University Press

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Vol.154 • No. 3 • 15 September 2010
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