Geodesic
Amenability of quadratic automaton groups
Gideon Amir1 orcid ; Omer Angel2 orcid ; Bálint Virág3 orcid
1Bar-Ilan University, Ramat Gan, Israel
2University of British Columbia, Vancouver, Canada
3University of Toronto, Toronto, Canada
Groups, geometry, and dynamics, Tome 19 (2025) no. 1, pp. 169-185

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DOI

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 0-ray. These bounds, combined with results of Juschenko et al. (2016), 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.
DOI : 10.4171/ggd/821
Classification : 05C81, 20E08, 43A07, 60B15
Mots-clés : amenability, automaton group, Schreier graph

Gideon Amir  1   ; Omer Angel  2   ; Bálint Virág  3

1 Bar-Ilan University, Ramat Gan, Israel
2 University of British Columbia, Vancouver, Canada
3 University of Toronto, Toronto, Canada 
Gideon Amir; Omer Angel; Bálint Virág. Amenability of quadratic automaton groups. Groups, geometry, and dynamics, Tome 19 (2025) no. 1, pp. 169-185. doi: 10.4171/ggd/821
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