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.
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://www.numdam.org/articles/10.1051/cocv/2013049/} }
TY - JOUR AU - Duong, Manh Hong AU - Laschos, Vaios AU - Renger, Michiel TI - Wasserstein gradient flows from large deviations of many-particle limits JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 1166 EP - 1188 VL - 19 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2013049/ DO - 10.1051/cocv/2013049 LA - en ID - COCV_2013__19_4_1166_0 ER -
%0 Journal Article %A Duong, Manh Hong %A Laschos, Vaios %A Renger, Michiel %T Wasserstein gradient flows from large deviations of many-particle limits %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 1166-1188 %V 19 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2013049/ %R 10.1051/cocv/2013049 %G en %F COCV_2013__19_4_1166_0
Duong, Manh Hong; Laschos, Vaios; Renger, Michiel. Wasserstein gradient flows from large deviations of many-particle limits. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 4, pp. 1166-1188. doi : 10.1051/cocv/2013049. http://www.numdam.org/articles/10.1051/cocv/2013049/
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