Gamma Convergence Approach For The Large Deviations Of The Density In Systems Of Interacting Diffusion Processes

Abstract : 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 , 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 (LDP) with a rate functional. We study the $\Gamma$-convergence of as $\rightarrow$ 0 and show it converges to the rate functional appearing in the Macroscopic Fluctuations Theory (MFT) for diffusive systems.
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https://hal.archives-ouvertes.fr/hal-02349973
Contributor : Raphael Chetrite <>
Submitted on : Tuesday, November 5, 2019 - 8:23:30 PM
Last modification on : Wednesday, November 6, 2019 - 1:49:43 AM

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Julien Barré, Cédric Bernardin, Raphael Chetrite, Yash Chopra, Mauro Mariani. Gamma Convergence Approach For The Large Deviations Of The Density In Systems Of Interacting Diffusion Processes. 2019. ⟨hal-02349973⟩

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