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October 2018 Equilibrium large deviations for mean-field systems with translation invariance
Julien Reygner
Ann. Appl. Probab. 28(5): 2922-2965 (October 2018). DOI: 10.1214/17-AAP1379


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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Julien Reygner. "Equilibrium large deviations for mean-field systems with translation invariance." Ann. Appl. Probab. 28 (5) 2922 - 2965, October 2018.


Received: 1 July 2017; Revised: 1 December 2017; Published: October 2018
First available in Project Euclid: 28 August 2018

zbMATH: 06974769
MathSciNet: MR3847977
Digital Object Identifier: 10.1214/17-AAP1379

Primary: 60F10 , 60J60 , 60K35

Keywords: Free energy , large deviations , McKean–Vlasov particle systems , mean-field systems , rank-based interacting diffusions

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.28 • No. 5 • October 2018
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