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

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 ).

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 ).

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1625

Russell Lyons 1; Yuval Peres 2; Xin Sun 3; Tianyi Zheng 4

1 Department of Mathematics, IndianaUniversity
2 Redmond, WA
3 Department of Mathematics, Columbia University
4 Department of Mathematics, UCSD
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     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},
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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, Serie 6, Volume 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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