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

Russell Lyons; Yuval Peres; Xin Sun; Tianyi Zheng

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

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 97-109.

Résumé
Abstract

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

Reçu le : 2017-05-09
Accepté le : 2018-01-16
Publié le : 2020-07-24

DOI : 10.5802/afst.1625

Affiliations des auteurs :

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

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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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},
     pages = {97--109},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
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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, 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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