A non-symmetric Kesten criterion and ratio limit theorem for random walks on amenable groups

2023/09/04 by Dougall, Rhiannon, Sharp, Richard · 3 citations
#20F65 #60G50 #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR)

paper · doi:10.48550/arxiv.2309.01766

Abstract

We consider random walks on countable groups. A celebrated result of Kesten says that the spectral radius of a symmetric walk (whose support generates the group as a semigroup) is equal to one if and only if the group is amenable. We give an analogue of this result for finitely supported walks which are not symmetric. We also conclude a ratio limit theorem for amenable groups.

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