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},
year = {2013},
publisher = {EDP Sciences},
volume = {19},
number = {4},
doi = {10.1051/cocv/2013049},
mrnumber = {3182684},
zbl = {1284.35011},
language = {en},
url = {https://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 - https://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 https://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, Tome 19 (2013) no. 4, pp. 1166-1188. doi: 10.1051/cocv/2013049
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