arXiv 1102.49792011-02-24math.PRmath.GR

Positive speed for high-degree automaton groups

Gideon Amir, Balint Virag

备注：: 18 pages, 4 figures
发表信息：: Groups, Geometry, and Dynamics, 2014, Vol. 8, Issue 1, 23-38
DOI：: 10.4171/GGD/215

英文摘要：

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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