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arXiv · 1910.04026

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

Julien Barré·Cedric Bernardin·Raphaël Chétrite·Yash Chopra·Mauro Mariani
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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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Julien Barré, Cedric Bernardin, Raphaël Chétrite, Yash Chopra, Mauro Mariani. 2019-10-09. Gamma Convergence Approach For The Large Deviations Of The Density In Systems Of Interacting Diffusion Processes. https://doi.org/10.1007/s10955-020-02598-w

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