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arXiv · 1010.0983

The rate of escape of random walks on polycyclic and metabelian groups

Russ Thompson
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Abstract

We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger form of subgroup distortion, which applies to non-finitely generated subgroups. Under this hypothesis, we compute the rate of escape for certain random walks on metabelian groups via a comparison to the toppling of a dissipative abelian sandpile.

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Russ Thompson. 2010-10-05. The rate of escape of random walks on polycyclic and metabelian groups. https://arxiv.org/abs/1010.0983

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