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We consider extended slow-fast systems of N interacting diffusions. Thetypical behavior of the empirical density is described by a nonlinearMcKean-Vlasov equation depending on , the scaling parameter separating the timescale of the slow variable from the time scale of the fast variable. Itsatypical behavior is encapsulated in a large N Large Deviation Principle (LDP)with a rate functional. We study the $\Gamma$-convergence of as $\rightarrow$ 0and show it converges to the rate functional appearing in the MacroscopicFluctuations Theory (MFT) for diffusive systems.

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