Amenability of quadratic automaton groups
Group Theory
2026-04-21 v1 Probability
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.
Keywords
Cite
@article{arxiv.2111.15206,
title = {Amenability of quadratic automaton groups},
author = {Gideon Amir and Omer Angel and Balint Virag},
journal= {arXiv preprint arXiv:2111.15206},
year = {2026}
}
Comments
20 pages, 3 figures