Invariance principle for diffusions in random environment

Struckmeier Struckmeier

doi:10.5488/cmp.11.2.275

Abstract

Invariance principle for diffusions in random environment

Highlights

We will show an invariance principle for the diffusive motion of a particle interacting with a random frozen configuration of infinitely many other particles in Rd
The interaction is described by a symmetric, translation invariant pair potential with repulsion at zero distance and proper decay at infinity
In this article we are going to show an invariance principle, i.e. convergence of a process to Brownian motion under a space-time scaling, for the diffusive motion of a particle interacting with infinitely many other particles in Rd, d 2

Summary

Introduction

In this article we are going to show an invariance principle, i.e. convergence of a process to Brownian motion under a space-time scaling, for the diffusive motion of a particle interacting with infinitely many other particles in Rd, d 2. To this end we will use a general approach developed by A. De Masi et al discussed this situation in the case of a positive, compactly-supported C∞ interaction potential De Masi et al formulated conditions on this environment process which imply an invariance principle for the original process (Xt)t 0

Configuration spaces

Construction of the process

Environment process and invariance principle