Large deviations for singularly interacting diffusions

Jasper Hoeksema; Thomas Holding; Mario Maurelli; Oliver Tse

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arXiv · 2002.01295

Large deviations for singularly interacting diffusions

Jasper Hoeksema·Thomas Holding·Mario Maurelli·Oliver Tse

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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.

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Jasper Hoeksema, Thomas Holding, Mario Maurelli, Oliver Tse. 2020-02-04. Large deviations for singularly interacting diffusions. https://arxiv.org/abs/2002.01295

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