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Critical Constants for Recurrence on Groups of Polynomial Growth

   
@article{EJP773,
	author = {David Revelle and Russ Thompson},
	title = {Critical Constants for Recurrence on Groups of Polynomial Growth},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {15},
	year = {2010},
	keywords = {nilpotent group; Schreier graph; random walk; recurrence; volume growth},
	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 $2$.},
	pages = {no. 23, 710-722},
	issn = {1083-6489},
	doi = {10.1214/EJP.v15-773},    
        url = {http://ejp.ejpecp.org/article/view/773}}