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Theses

Marche aléatoire sur un groupe : propriétés dimensionnelles de la mesure harmonique

Abstract : This thesis deals with the harmonic measure associated with a random walk on a hy­perbolic group or a discrete subgroup of a semisimple group. In both contexts, the groups are equiped with a natural geometric boundary, which carries the harmonic mea­sure. We consider the relations between this measure and the metric structure of the boundary through the study of its dimension. In each context, we establish an upper bound of the dimension of the harmonic measure in term of the asymptotic entropy and of the rate of escape of the random walk. This upper bound allows us to construct harmonic measures with small dimension. One of our main results is a consequence of this construction: the harmonic measure associated with a random walk on a lattice in a semisimple group can be singular with respect to the Haar measure on the space of complete flags.
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https://tel.archives-ouvertes.fr/tel-00008442
Contributor : Marie-Annick Guillemer <>
Submitted on : Thursday, February 10, 2005 - 4:58:12 PM
Last modification on : Thursday, January 7, 2021 - 4:24:37 PM
Long-term archiving on: : Friday, September 14, 2012 - 11:05:32 AM

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  • HAL Id : tel-00008442, version 1

Citation

Vincent Le Prince. Marche aléatoire sur un groupe : propriétés dimensionnelles de la mesure harmonique. Mathématiques [math]. Université Rennes 1, 2004. Français. ⟨tel-00008442⟩

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