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Large deviations for empirical measures of mean-field Gibbs measures. (English) Zbl 07157644
Summary: 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.

##### MSC:
 60F10 Large deviations 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C22 Interacting particle systems in time-dependent statistical mechanics
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