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

Russell Lyons; Yuval Peres; Xin Sun; Tianyi Zheng

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arXiv · 1705.03576

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

Russell Lyons·Yuval Peres·Xin Sun·Tianyi Zheng

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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 $O(r^{11/2})$.

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Russell Lyons, Yuval Peres, Xin Sun, Tianyi Zheng. 2017-05-10. Occupation measure of random walks and wired spanning forests in balls of Cayley graphs. https://arxiv.org/abs/1705.03576

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