Algebraic structure of groups reflected in random walk distributions
Murray J. Elder, Cameron Rogers · arXiv (Cornell University) · 2016
For each measure $\mu$ on a finitely generated group, we define a set $A_\mu$ consisting of those group elements visited asymptotically as often as the identity by a random walk motivated by $\mu$. When $\mu$ is symmetric and non-periodic, $A_\mu$ is proved to be an amenable subgroup. Examples are given for which $A_\mu$ depends on the measure. We state several conjectures connecting $A_\mu$ with the amenable radical. We then extend standard results to obtain an explicit F{\o}lner sequence from random walk distributions.