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

2010/10/05 by Russ Thompson, Thompson, Russ
Mathematics · #20F65 #60B15 #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR) #math.GR #math.PR #msc:20F65 #msc:60B15

paper · pdf · doi:10.48550/arxiv.1010.0983

19 pages, 1 figure

arxiv created 2011/09/13 · arxiv updated 2011/09/14

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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