Large deviations for singularly interacting diffusions

2020/02/04 by Hoeksema, Jasper, Holding, Thomas, Maurelli, Mario +1
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2002.01295

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.

Related

• Large deviations for diffusions interacting through their ranks
• Large deviations of reflected weakly interacting particle systems
• Large Deviation Principle for Interacting Brownian Motions
• Large deviations for interacting multiscale particle systems
• Moderate deviations for fully coupled multiscale weakly interacting particle systems