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Positive speed for high-degree automaton groups

By Gideon Amir and Balint Virag

Abstract

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 tran- sient.Comment: 18 pages, 4 figure

Topics: Mathematics - Probability, Mathematics - Group Theory, 60B15, 20E08, 05C21, 05C81
Year: 2011
DOI identifier: 10.4171/GGD/215
OAI identifier: oai:arXiv.org:1102.4979
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