Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Large deviations for diffusing particles with electrostatic repulsion


Code(s) de Classification MSC:

Résumé: We apply the hydrodynamics approach to study the large deviations properties of the McKean-Vlasov model with singular interactions introduced by Cépa and Lépingle in [4]. In a general setting, we study the action functional and obtain complete upper bounds and exponential tightness. We relate the study of the lower bounds to the uniqueness problem of a class of nonlinear equations generalizing the one studied in [4]. In the case of interacting Orstein-Ulhenbeck particles, we obtain a general uniqueness statement, which improves the analogous result of Cabannal-Duvillard and Guionnet [1] for the Hermitian Brownian motion model, and we deduce some partial lower bounds.

Mots Clés: McKean-Vlasov model ; singular interactions ; large deviations

Date: 2002-11-12

Prépublication numéro: PMA-771

Pdf file : PMA-771.pdf