Wasserstein gradient flows from large deviations of many-particle limits
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1166-1188.

We study the Fokker-Planck equation as the many-particle limit of a stochastic particle system on one hand and as a Wasserstein gradient flow on the other. We write the path-space rate functional, which characterises the large deviations from the expected trajectories, in such a way that the free energy appears explicitly. Next we use this formulation via the contraction principle to prove that the discrete time rate functional is asymptotically equivalent in the Gamma-convergence sense to the functional derived from the Wasserstein gradient discretization scheme.

DOI : 10.1051/cocv/2013049
Classification : 35A15, 5Q84
Mots-clés : Wasserstein, gradient flows, Fokker-Planck, gamma-convergence, large deviations 
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     title = {Wasserstein gradient flows from large deviations of many-particle limits},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1166--1188},
     publisher = {EDP-Sciences},
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Duong, Manh Hong; Laschos, Vaios; Renger, Michiel. Wasserstein gradient flows from large deviations of many-particle limits. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1166-1188. doi : 10.1051/cocv/2013049. http://archive.numdam.org/articles/10.1051/cocv/2013049/

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