Brownian motion and parabolic Anderson model in a renormalized Poisson potential

Chen, Xia; Kulik, Alexey M.

Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) no. 3, pp. 631-660.

Nous présentons une méthode de renormalisation pour construire certains modèles de potentiels aléatoires dans un nuage Poissonnien qui sont physiquement plus réalistes. Nous obtenons le mouvement brownien dans un potentiel aléatoire renormalisé et les modèles d'Anderson paraboliques associés. Par exemple, avec cette renormalisation, nous pouvons construire rigoureusement des modèles consistants avec la loi de la gravitation de Newton.

A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton's law of universal attraction can be rigorously constructed.

Classification : 60J45, 60J65, 60K37, 60K37, 60G55
Mots clés : renormalization, Poisson field, brownian motion in Poisson potential, parabolic Anderson model, Newton's law of universal attraction

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