Large deviations for singularly interacting diffusions
Probability
2020-07-02 v2
Abstract
In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the associated McKean-Vlasov equation. Along the way, we prove an extended version of the Varadhan Integral Lemma for a discontinuous change of measure and subsequently an LDP for Gibbs and Gibbs-like measures with singular potentials.
Cite
@article{arxiv.2002.01295,
title = {Large deviations for singularly interacting diffusions},
author = {Jasper Hoeksema and Thomas Holding and Mario Maurelli and Oliver Tse},
journal= {arXiv preprint arXiv:2002.01295},
year = {2020}
}