A note on exit time for anchored isoperimetry

Delmotte, Thierry; Rau, Clément

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Numéro Spécial : Conférence “Talking Across Fields” du 24 au 28 mars 2014 à l’Institut de Mathématiques de Toulouse, Tome 24 (2015) no. 4, pp. 817-835.

Soit ${\left(X_n\right)}_{n\ge 0}$ une marche aléatoire réversible sur un graphe $G$ vérifiant une inégalité isopérimétrique ancrée. Nous obtenons une majoration du temps de sortie de tout ensemble connexe contenant un point ancre (et du temps de passage dans le cas transient) de la marche $X$.

Let ${\left(X_n\right)}_{n\ge 0}$ be a reversible random walk on a graph $G$ satisfying an anchored isoperimetric inequality. We give upper bounds for exit time (and occupation time in transient case) by $X$ of any set which contains the root. This article covers many results of [11].

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