Quenched large deviations for interacting diffusions in random media

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.

arXiv comment34 pages

References in corpus (8)

• Novel type of phase transition in a system of self-driven particles
• Macroscopic limits and phase transition in a system of self-propelled particles
• Large deviation properties of weakly interacting processes via weak convergence methods
• Process-level quenched large deviations for random walk in random environment
• A simple mean field model for social interactions: dynamics, fluctuations, criticality
• Quenched limits and fluctuations of the empirical measure for plane rotators in random media
• Asymptotics of mean-field $O(N)$ models
• Large deviations of continuous regular conditional probabilities

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