Positive speed for high-degree automaton groups

  • Gideon Amir

    Bar-Ilan University, Ramat Gan, Israel
  • Bálint Virág

    University of Toronto, Toronto, Canada


Mother groups are the basic building blocks for polynomial automaton groups. We show that, in contrast with mother groups of degree 0 or 1, any bounded, symmetric, generating random walk on the mother groups of degree at least 3 has positive speed. The proof is based on an analysis of resistance in fractal mother graphs. We give upper bounds on resistances in these graphs, and show that infinite versions are transient.

Cite this article

Gideon Amir, Bálint Virág, Positive speed for high-degree automaton groups. Groups Geom. Dyn. 8 (2014), no. 1, pp. 23–38

DOI 10.4171/GGD/215