On amenability of automata groups

By Laurent Bartholdi, Vadim A. Kaimanovich, Volodymyr V. Nekrashevych. 2008

115 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a9199edf8ea5f2439df962ad45db5389aa02730a

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In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Milnor's Problem on the Growth of Groups and its Consequences (2011, methodology): “Tree-like constructions and techniques of self-similar groups naturally leading to such examples were explored by V. Nekrashevych [Nek10].”
Amenability of linear-activity automaton groups (2009, methodology): “2006), Question 16.74, and also in Guido’s book of conjectures (2008), Conjecture 35.9. Our paper builds on previous work in the theory, including Bartholdi and Vir´ag (2005), Kaimanovich (2005), and Bartholdi et al. (2008). The ﬁrst part of the proof is to construct a family of linear-activity auto”