Positive speed for high-degree automaton groups

Details Positive speed for high-degree automaton groups Positive speed for high-degree automaton groups

2011-02-24

arxiv.org/abs/1102.4979v1

Mathematics

Probability

18 pages, 4 figures

Scientific paper

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.

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