Amenability of quadratic automaton groups
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.
Authors
- Gideon Amir (ORCID: https://orcid.org/0000-0001-7738-0441)
- Omer Angel (ORCID: https://orcid.org/0000-0002-6451-8242)
- Bálint Virág (ORCID: https://orcid.org/0000-0002-9671-773X)
Institutions
- Bar-Ilan University (IL)
- University of British Columbia (CA)
- University of Toronto (CA)
Publication Details
- Journal
- Groups Geometry and Dynamics
- Published
- 2024-10-10
- DOI
- https://doi.org/10.4171/ggd/821
- Citations
- 1
- Primary Topic
- semigroups and automata theory
- Type
- article
- Field-Weighted Citation Impact
- 0.36
Funders
- Israel Science Foundation
- Natural Sciences and Engineering Research Council of Canada