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Homogenization of Ornstein-Uhlenbeck Process in Random Environment

Benabou, Gaël (2006), Homogenization of Ornstein-Uhlenbeck Process in Random Environment, Communications in Mathematical Physics, 266, 3, p. 699-714. http://dx.doi.org/10.1007/s00220-006-0046-9

Type
Article accepté pour publication ou publié
Date
2006
Nom de la revue
Communications in Mathematical Physics
Volume
266
Numéro
3
Éditeur
Springer
Pages
699-714
Identifiant publication
Métadonnées
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Auteur(s)
Benabou, Gaël
Résumé (EN)
We consider a tracer particle moving in a random environment. The velocity of the tracer is modelled by an Ornstein-Uhlenbeck process which takes into account inertia and friction. The medium results in a possibly unbounded random potential. We prove an invariance principle for this kind of motion. The method used is generalized in order to obtain a central limit theorem for a large class of process, the most interesting application being a tagged particle in a medium of infinitely many Ornstein-Uhlenbeck particles.
Mots-clés
random environment; tracer particle