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 Γ-convergence of as → 0 and show it converges to the rate functional appearing in the Macroscopic Fluctuations Theory (MFT) for diffusive systems.
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Submitted on : Wednesday, October 9, 2019 - 11:19:49 AM
Last modification on : Thursday, October 10, 2019 - 1:30:48 AM

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  • HAL Id : hal-02309363, version 1
  • ARXIV : 1910.04026

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Julien Barré, Cedric Bernardin, Raphaël Chétrite, Yash Chopra, Mauro Mariani. GAMMA CONVERGENCE APPROACH FOR THE LARGE DEVIATIONS OF THE DENSITY IN SYSTEMS OF INTERACTING DIFFUSION PROCESSES. 2019. ⟨hal-02309363⟩

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