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Article dans une revue

Equilibrium large deviations for mean-field systems with translation invariance

Abstract : We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large deviation principles for its empirical measure at equilibrium. Our study covers the cases of McKean-Vlasov particle systems without external potential, and systems of rank-based interacting diffusions. Depending on the strength of the interaction, the large deviation principles are stated in the space of centered probability measures endowed with the Wasserstein topology of appropriate order, or in the orbit space of the action of translations on probability measures. An application to the study of atypical capital distribution is detailed.
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https://hal-enpc.archives-ouvertes.fr/hal-01546442
Contributeur : Julien Reygner <>
Soumis le : jeudi 7 décembre 2017 - 11:32:35
Dernière modification le : vendredi 25 octobre 2019 - 15:38:07

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Julien Reygner. Equilibrium large deviations for mean-field systems with translation invariance. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2018, 28 (5), pp.2922-2965. ⟨10.1214/17-AAP1379⟩. ⟨hal-01546442v2⟩

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