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 $2$.
Citation
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
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