EQUILIBRIUM LARGE DEVIATIONS FOR MEAN-FIELD SYSTEMS WITH TRANSLATION INVARIANCE

• 成果类型: Article
• 署名作者: Reygner, Julien
• 署名单位: Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Gustave-Eiffel
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1379
• 发表日期: 2018
• 页码: 2922-2965
• 关键词: self-stabilizing processes; granular media equations; propagation; CONVERGENCE; DIFFUSIONS; particles; approximation; EXISTENCE; chaos; limit

摘要

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.