On the diffusive behavior of isotropic diffusions in a random environment

Alain-Sol Sznitman; Ofer Zeitouni

doi:10.1016/j.crma.2004.07.012

Probability Theory

On the diffusive behavior of isotropic diffusions in a random environment
[Comportement asymptotique de diffusions isotropes en milieu aléatoire.]

Présenté par : Jean-Michel Bismut

Alain-Sol Sznitman ¹ ; Ofer Zeitouni ^2,³

¹ Departement Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland
² Department of Mathematics, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, MN 55455, USA
³ Departments of Electrical Engineering and of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel

Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 429-434.

Résumé
Abstract

Nous présentons ici des résultats sur le comportement asymptotique de diffusions isotropes en milieu aléatoire, qui sont de petites perturbations du mouvement brownien. Lorsque la dimension de l'espace est trois ou plus nous prouvons un principe d'invariance et la transience de la diffusion. Nos méthodes s'appliquent aussi à des problèmes d'homogénéisation en milieu aléatoire.

We present here results concerning the asymptotic behavior of isotropic diffusions in random environment that are small perturbations of Brownian motion. When the space dimension is three or more we prove an invariance principle as well as transience. Our methods also apply to questions of homogenization in random media.

Reçu le : 2004-06-09
Accepté le : 2004-07-12
Publié le : 2004-09-09

DOI : 10.1016/j.crma.2004.07.012

Affiliations des auteurs :

Alain-Sol Sznitman ¹ ; Ofer Zeitouni ^{2, 3}

¹ Departement Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland
² Department of Mathematics, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, MN 55455, USA
³ Departments of Electrical Engineering and of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel

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Alain-Sol Sznitman; Ofer Zeitouni. On the diffusive behavior of isotropic diffusions in a random environment. Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 429-434. doi : 10.1016/j.crma.2004.07.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.012/

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