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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Abstract

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.

Résumé

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.

Article information

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

Dates
First available in Project Euclid: 26 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1340714866

Digital Object Identifier
doi:10.1214/11-AIHP419

Mathematical Reviews number (MathSciNet)
MR2976557

Zentralblatt MATH identifier
1279.60106

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.aihp/1340714866.


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