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

@article{Lyons2017OccupationMO,
  title={Occupation measure of random walks and wired spanning forests in balls of Cayley graphs},
  author={Russell Lyons and Yuval Peres and Xin Sun and Tianyi Zheng},
  journal={arXiv: Probability},
  year={2017}
}
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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