Large Deviation Principle for Interacting Brownian Motions

TL;DR

This paper establishes a Large Deviation Principle for the empirical process of a system of locally interacting Brownian motions in nonequilibrium, extending known results from lattice systems to diffusion-type particle systems.

Contribution

It provides the first Large Deviation Principle for diffusion-type interacting particle systems, expanding the scope of such principles beyond lattice models.

Findings

Proves the Large Deviation Principle for interacting Brownian motions.

Extends large deviation results to diffusion-type systems.

First such result for this class of particle systems.

Abstract

We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple exclusion process and zero-range process. Therefore, we have achieved the third result in this context and moreover the first result for the diffusion-type interacting particle system.