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A non-symmetric Kesten criterion and ratio limit theorem for random walks on amenable groups
Rhiannon Dougall, Richard Sharp · 2023-09-05 · via math.PR updates on arXiv.org

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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