A Non-Symmetric Kesten Criterion and Ratio Limit Theorem for Random Walks on Amenable Groups - Dougall, Rhiannon; Sharp, Richard (International Mathematics Research Notices, 2024)
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 walks that are not symmetric. We also conclude a ratio limit theorem for amenable groups.
Keywords: General Mathematics