Published 2020
| Version v1
Journal article
From fluctuating kinetics to fluctuating hydrodynamics: a $\Gamma$-Convergence of large deviations functionals approach
- Others:
- Institut Denis Poisson (IDP) ; Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)
- Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
- Vysšaja škola èkonomiki = National Research University Higher School of Economics [Moscow] (HSE)
- ANR-15-IDEX-0001,UCA JEDI,Idex UCA JEDI(2015)
- ANR-15-CE40-0020,LSD,Modèles stochastiques en grande dimension pour la physique statistique hors équilibre(2015)
Description
We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean–Vlasov equation depending on ε, the scaling parameter separating the time scale of the slow variable from the time scale of the fast variable. Its atypical behavior is encapsulated in a large N Large Deviation Principle with a rate functional Iε. We study the Γ-convergence of Iε as ε→0 and show it converges to the rate functional appearing in the Macroscopic Fluctuations Theory for diffusive systems.
Abstract
International audience
Additional details
- URL
- https://hal.archives-ouvertes.fr/hal-02309363
- URN
- urn:oai:HAL:hal-02309363v1
- Origin repository
- UNICA