ParkinsonFranceV1, Main, Exploration, bibRecord, 000087

Asymptotic entropy of random walks on Fuchsian buildings and Kac-Moody groups

Identifieur interne : 000087 ( Main/Exploration ); précédent : 000086; suivant : 000088

Asymptotic entropy of random walks on Fuchsian buildings and Kac-Moody groups

Auteurs : Lorenz A. Gilch [Autriche] ; Sebastian Mueller [France] ; James Parkinson [Australie]

Source :

RBID : Hal:hal-01285406

Abstract

In this article we prove existence of the asymptotic entropy for isotropic random walks on regular Fuchsian buildings. Moreover, we give formulae for the asymptotic entropy, and prove that it is equal to the rate of escape of the random walk with respect to the Green distance. When the building arises from a Fuchsian Kac-Moody group our results imply results for random walks induced by bi-invariant measures on these groups, however our results are proven in the general setting without the assumption of any group acting on the building. The main idea is to consider the retraction of the isotropic random walk onto an apartment of the building, to prove existence of the asymptotic entropy for this retracted walk, and to `lift' this in order to deduce the existence of the entropy for the random walk on the building.

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https://hal.archives-ouvertes.fr/hal-01285406

Affiliations:

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Le document en format XML

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<front><div type="abstract" xml:lang="en">In this article we prove existence of the asymptotic entropy for isotropic random walks on regular Fuchsian buildings. Moreover, we give formulae for the asymptotic entropy, and prove that it is equal to the rate of escape of the random walk with respect to the Green distance. When the building arises from a Fuchsian Kac-Moody group our results imply results for random walks induced by bi-invariant measures on these groups, however our results are proven in the general setting without the assumption of any group acting on the building. The main idea is to consider the retraction of the isotropic random walk onto an apartment of the building, to prove existence of the asymptotic entropy for this retracted walk, and to `lift' this in order to deduce the existence of the entropy for the random walk on the building.</div>
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Asymptotic entropy of random walks on Fuchsian buildings and Kac-Moody groups

Asymptotic entropy of random walks on Fuchsian buildings and Kac-Moody groups

Source :

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri