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Homogenization of Ornstein-Uhlenbeck Process in Random Environment

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Abstract

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.

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Authors and Affiliations

  1. Ceremade, UMR CNRS 7534, Université Paris IX - Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Gaël Benabou

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  1. Gaël Benabou
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Correspondence to Gaël Benabou.

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Communicated by H. Spohn

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Benabou, G. Homogenization of Ornstein-Uhlenbeck Process in Random Environment. Commun. Math. Phys. 266, 699–714 (2006). https://doi.org/10.1007/s00220-006-0046-9

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