Harmonic measures versus quasiconformal measures for hyperbolic groups
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 44 (2011) no. 4, pp. 683-721.

We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.

On établit une formule de la dimension de la mesure harmonique d'une marche aléatoire de loi de support fini et symétrique sur un groupe hyperbolique. On caractérise aussi les lois pour lesquelles la dimension est maximale. Notre approche repose sur la distance de Green, une distance qui permet de développer un point de vue géométrique sur les marches aléatoires et, en particulier, d'interpréter les mesures harmoniques comme des mesures quasiconformes.

DOI: 10.24033/asens.2153
Classification: 20F67,  60B15,  11K55,  20F69,  28A75,  60J50,  60J65
Keywords: hyperbolic groups, random walks on groups, harmonic measures, quasiconformal measures, dimension of a measure, Martin boundary, brownian motion, Green metric
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Blachère, Sébastien; Haïssinsky, Peter; Mathieu, Pierre. Harmonic measures versus quasiconformal measures for hyperbolic groups. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 44 (2011) no. 4, pp. 683-721. doi : 10.24033/asens.2153. http://archive.numdam.org/articles/10.24033/asens.2153/

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