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

Abstract

We show that for finite-range, symmetric random walks on general transient Cayley graphs, the expected occupation time of any given ball of radius $r$ is $O(r^{5/2})$.. We also study the volume-growth property of the wired spanning forests on general Cayley graphs, showing that the expected number of vertices in the component of the identity inside any given ball of radius $r$ is $O(r^{11/2})$.

arXiv comment15 pages, 1 figure; T.Zheng is added as an author due to her key contribution to the improvement on the exponents from the first version

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