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

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

2010-10-05

arxiv.org/abs/1010.0983v2

Mathematics

Probability

19 pages, 1 figure

Scientific paper

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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