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 a LDP for Gibbs and Gibbs -like measures with singular potentials.
Large deviations for singularly interacting diffusions
Maurelli, Mario;
2024-01-01
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 a LDP for Gibbs and Gibbs -like measures with singular potentials.File in questo prodotto:
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