Quenched large deviations for interacting diffusions in random media

TL;DR

This paper establishes a quenched large deviation principle for the empirical measure of mean-field interacting diffusions in a fixed random environment, revealing a disorder-independent rate function.

Contribution

It provides the first quenched LDP for interacting diffusions in random media, with a novel rate function differing from the averaged case.

Findings

LDP holds for every fixed environment realization

Rate function is independent of the disorder

Results extend to empirical flow and local measures

Abstract

The aim of the paper is to establish a large deviation principle (LDP) for the empirical measure of mean-field interacting diffusions in a random environment. The point is to derive such a result once the environment has been frozen (quenched model). The main theorem states that a LDP holds for every realization of the environment, with a rate function that does not depend on the disorder and is different from the rate function in the averaged model. Similar results concerning the empirical flow and local empirical measures are provided.