Random walks under slowly varying moment conditions on groups of polynomial volume growth
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 4, pp. 837-855.

Let G be a finitely generated group of polynomial volume growth equipped with a word-length |·|. The goal of this paper is to develop techniques to study the behavior of random walks driven by symmetric measures μ such that, for any ϵ>0, |·| ϵ μ=. In particular, we provide a sharp lower bound for the return probability in the case when μ has a finite weak-logarithmic moment.

Soit G un groupe finiment engendré, à croissance polynomiale du volume et muni de la distance des mots associée à un ensemble donné de générateurs. Le but de ce travail est de développer des techniques qui permettent l’étude de marches aléatoires associées à des mesures de probabilité symetriques, μ, telles que, pout tout ϵ>0, |·| ϵ μ=. En particulier, nous donnons une borne inférieure optimale pour la probabilité de retour dans le cas où μ a un moment logarithmique de type faible fini.

DOI: 10.5802/afst.1467

Laurent Saloff-Coste 1; Tianyi Zheng 2

1 Department of Mathematics, Cornell University
2 Department of Mathematics, Stanford University
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Laurent Saloff-Coste; Tianyi Zheng. Random walks under slowly varying moment conditions on groups of polynomial volume growth. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 4, pp. 837-855. doi : 10.5802/afst.1467. https://afst.centre-mersenne.org/articles/10.5802/afst.1467/

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