Occupation measure of random walks and wired spanning forests in balls of Cayley graphs

摘要

We show that for finite-range, symmetric random walks on general transientCayley graphs, the expected occupation time of any given ball of radius $r$ is$O(r^3)$. We also study the volume-growth property of the wired spanningforests on general Cayley graphs, showing that the expected number of verticesin the component of the identity inside any given ball of radius $r$ is$O(r^6)$.