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2010 Critical Constants for Recurrence on Groups of Polynomial Growth
David Revelle, Russ Thompson
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Electron. J. Probab. 15: 710-722 (2010). DOI: 10.1214/EJP.v15-773

Abstract

The critical constant for recurrence, $c_{rt}$, is an invariant of the quotient space $H/G$ of a finitely generated group. The constant is determined by the largest moment a probability measure on $G$ can have without the induced random walk on $H/G$ being recurrent. We present a description of which subgroups of groups of polynomial volume growth are recurrent. Using this we show that for such recurrent subgroups $c_{rt}$ corresponds to the relative growth rate of $H$ in $G$, and in particular $c_{rt}$ is either $0$, $1$ or $2$.

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David Revelle. Russ Thompson. "Critical Constants for Recurrence on Groups of Polynomial Growth." Electron. J. Probab. 15 710 - 722, 2010. https://doi.org/10.1214/EJP.v15-773

Information

Accepted: 16 April 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60006
MathSciNet: MR2650779
Digital Object Identifier: 10.1214/EJP.v15-773

Subjects:
Primary: 60B15
Secondary: 20F65

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Vol.15 • 2010
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