Brownian motion and parabolic Anderson model in a renormalized Poisson potential

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. © Association des Publications de l'Institut Henri Poincaré, 2012.