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 $\to$ 0 and show it converges to the rate functional appearing in the Macroscopic Fluctuations Theory (MFT) for diffusive systems.

References in corpus (17)

• Novel type of phase transition in a system of self-driven particles
• The large deviation approach to statistical mechanics
• Macroscopic fluctuation theory
• Hydrodynamics of self-propelled hard rods
• A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms
• Long-time behaviour and phase transitions for the McKean--Vlasov equation on the torus
• Freidlin-Wentzell LDP in path space for McKean-Vlasov equations and the Functional Iterated Logarithm Law
• Perturbative calculation of quasi-potential in non-equilibrium diffusions: a mean-field example
• Motility-induced phase separation of active particles in the presence of velocity alignment
• Hamiltonian and Brownian systems with long-range interactions: V. Stochastic kinetic equations and theory of fluctuations
• A Law of Large Numbers and Large Deviations for interacting diffusions on Erdős-Rényi graphs
• Large Deviations in Fast-Slow Systems
• Long-range correlations in a locally driven exclusion process
• Density large deviations for multidimensional stochastic hyperbolic conservation laws
• Full metastable asymptotic of the Fisher information
• Equilibrium large deviations for mean-field systems with translation invariance
• A proof of the mean-field limit for $\lambda$-convex potentials by $\Gamma$-Convergence

Cited by in corpus (2)

• On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions
• Full $\Gamma$-expansion of reversible Markov chains level two large deviations rate functionals