Geodesic
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

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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
Keywords: Wasserstein, gradient flows, Fokker-Planck, gamma-convergence, large deviations 
@article{COCV_2013__19_4_1166_0,
     author = {Duong, Manh Hong and Laschos, Vaios and Renger, Michiel},
     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},
     volume = {19},
     number = {4},
     year = {2013},
     doi = {10.1051/cocv/2013049},
     mrnumber = {3182684},
     zbl = {1284.35011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013049/}
}
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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

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