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

Rhiannon Dougall; Richard Sharp

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arXiv · 2309.01766

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

Rhiannon Dougall·Richard Sharp

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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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Rhiannon Dougall, Richard Sharp. 2023-09-04. A non-symmetric Kesten criterion and ratio limit theorem for random walks on amenable groups. https://arxiv.org/abs/2309.01766

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