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arXiv · 2111.15206

Amenability of quadratic automaton groups

Gideon Amir·Omer Angel·Balint Virag
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Abstract

We give lower bounds for the electrical resistance between vertices in the Schreier graphs of the action of the linear (degree 1) and quadratic (degree 2) mother groups on the orbit of the zero ray. These bounds, combined with results of \cite{JNS} show that every quadratic activity automaton group is amenable. The resistance bounds use an apparently new "weighted" version of the Nash-Williams criterion which may be of independent interest.

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Gideon Amir, Omer Angel, Balint Virag. 2021-11-30. Amenability of quadratic automaton groups. https://doi.org/10.4171/ggd%2F821

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