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Random walks under slowly varying moment conditions on groups of polynomial volume growth
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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.

Published online : 2016-01-21
@article{AFST_2015_6_24_4_837_0,
     author = {Laurent Saloff-Coste and Tianyi Zheng},
     title = {Random walks under slowly varying moment conditions on groups of polynomial volume growth},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 24},
     number = {4},
     year = {2015},
     pages = {837-855},
     language = {en},
     url={afst.centre-mersenne.org/item/AFST_2015_6_24_4_837_0/}
}
Saloff-Coste, Laurent; Zheng, Tianyi. 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. https://afst.centre-mersenne.org/item/AFST_2015_6_24_4_837_0/

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