We show that for finite-range, symmetric random walks on general transient Cayley graphs, the expected occupation time of any given ball of radius is . 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 is .
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 vaut . 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 vaut .
Accepted:
Published online:
Russell Lyons 1; Yuval Peres 2; Xin Sun 3; Tianyi Zheng 4
@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/} }
TY - JOUR AU - Russell Lyons AU - Yuval Peres AU - Xin Sun AU - Tianyi Zheng TI - Occupation measure of random walks and wired spanning forests in balls of Cayley graphs JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2020 SP - 97 EP - 109 VL - 29 IS - 1 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1625/ DO - 10.5802/afst.1625 LA - en ID - AFST_2020_6_29_1_97_0 ER -
%0 Journal Article %A Russell Lyons %A Yuval Peres %A Xin Sun %A Tianyi Zheng %T Occupation measure of random walks and wired spanning forests in balls of Cayley graphs %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2020 %P 97-109 %V 29 %N 1 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1625/ %R 10.5802/afst.1625 %G en %F AFST_2020_6_29_1_97_0
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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