A non-symmetric Kesten criterion and ratio limit theorem for random walks on amenable groups
Group Theory
2023-09-06 v1 Probability
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.
Cite
@article{arxiv.2309.01766,
title = {A non-symmetric Kesten criterion and ratio limit theorem for random walks on amenable groups},
author = {Rhiannon Dougall and Richard Sharp},
journal= {arXiv preprint arXiv:2309.01766},
year = {2023}
}