From fluctuating kinetics to fluctuating hydrodynamics: a $\Gamma$-Convergence of large deviations functionals approach
Résumé
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.
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