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February 2003 Moderate deviations for mean-field Gibbs measures
Peter Eichelsbacher, Tim Zajic
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Bernoulli 9(1): 67-95 (February 2003). DOI: 10.3150/bj/1068129011


We present a moderate-deviations principle around non-degenerate attractors of the empirical measure of random variables distributed according to a mean-field Gibbs measure. We state a result for a large class of densities of the Gibbs measure. This result is an application of a rank-dependent moderate-deviations principle for a collection of $U$-empirical measures. The results are applied for diffusion processes with mean-field interaction leading to a McKean--Vlasov limit, and to the Curie--Weiss model.


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Peter Eichelsbacher. Tim Zajic. "Moderate deviations for mean-field Gibbs measures." Bernoulli 9 (1) 67 - 95, February 2003.


Published: February 2003
First available in Project Euclid: 6 November 2003

zbMATH: 1029.60021
MathSciNet: MR1963673
Digital Object Identifier: 10.3150/bj/1068129011

Keywords: $U$-statistics , Curie-Weiss model , Decoupling , Gibbs measures , Langevin dynamics , Mean field , Moderate deviations

Rights: Copyright © 2003 Bernoulli Society for Mathematical Statistics and Probability

Vol.9 • No. 1 • February 2003
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