Duke Mathematical Journal

On amenability of automata groups

Laurent Bartholdi, Vadim A. Kaimanovich, and Volodymyr V. Nekrashevych

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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.

Article information

Duke Math. J., Volume 154, Number 3 (2010), 575-598.

First available in Project Euclid: 7 September 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20E08: Groups acting on trees [See also 20F65]
Secondary: 20P05: Probabilistic methods in group theory [See also 60Bxx] 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 43A07: Means on groups, semigroups, etc.; amenable groups 60G50: Sums of independent random variables; random walks


Bartholdi, Laurent; Kaimanovich, Vadim A.; Nekrashevych, Volodymyr V. On amenability of automata groups. Duke Math. J. 154 (2010), no. 3, 575--598. doi:10.1215/00127094-2010-046. https://projecteuclid.org/euclid.dmj/1283865313

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