Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Brownian motion and parabolic Anderson model in a renormalized Poisson potential

Xia Chen and Alexey M. Kulik

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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.


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.

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Ann. Inst. H. Poincaré Probab. Statist., Volume 48, Number 3 (2012), 631-660.

First available in Project Euclid: 26 June 2012

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Zentralblatt MATH identifier

Primary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60J65: Brownian motion [See also 58J65] 60K37: Processes in random environments 60K37: Processes in random environments 60G55: Point processes

Renormalization Poisson field Brownian motion in Poisson potential Parabolic Anderson model Newton’s law of universal attraction


Chen, Xia; Kulik, Alexey M. Brownian motion and parabolic Anderson model in a renormalized Poisson potential. Ann. Inst. H. Poincaré Probab. Statist. 48 (2012), no. 3, 631--660. doi:10.1214/11-AIHP419.

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