Large deviations for empirical measures of mean-field Gibbs measures

Wei Liu and Liming Wu

Stochastic Processes and their Applications, 2020, vol. 130, issue 2, 503-520

Abstract: In this paper, we show that the empirical measure of mean-field model satisfies the large deviation principle with respect to the weak convergence topology or the stronger Wasserstein metric, under the strong exponential integrability condition on the negative part of the interaction potentials. In contrast to the known results we prove this without any continuity or boundedness condition on the interaction potentials. The proof relies mainly on the law of large numbers and the exponential decoupling inequality of de la Peña for U-statistics.

Keywords: Large deviations; Empirical measure; U-statistics; Interacting particle systems; McKean–Vlasov equation; Mean-field Gibbs measure (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.01.008

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