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Occupation measure of random walks and wired spanning forests in balls of Cayley graphs
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 97-109.

On montre que toute marche aléatoire symétrique à pas bornés sur un graphe de Cayley transitoire satisfait que l’espérance du temps d’occupation d’une boule quelconque de rayon r vaut O(r 5/2 ). On étudie aussi la croissance du volume des forêts recouvrantes câblées dans les graphes de Cayley généraux, en montrant que l’espérance du nombre de sommets appartenant à la composante connexe de l’identité dans une boule quelconque de rayon r vaut O(r 11/2 ).

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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DOI : https://doi.org/10.5802/afst.1625
@article{AFST_2020_6_29_1_97_0,
     author = {Russell Lyons and Yuval Peres and Xin Sun and Tianyi Zheng},
     title = {Occupation measure of random walks and wired spanning forests in balls of Cayley graphs},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {97--109},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 29},
     number = {1},
     year = {2020},
     doi = {10.5802/afst.1625},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1625/}
}
Russell Lyons; Yuval Peres; Xin Sun; Tianyi Zheng. Occupation measure of random walks and wired spanning forests in balls of Cayley graphs. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 97-109. doi : 10.5802/afst.1625. https://afst.centre-mersenne.org/articles/10.5802/afst.1625/

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