Volume 19, Number 4, October-December 2013
|Page(s)||1166 - 1188|
|Published online||13 August 2013|
Wasserstein gradient flows from large deviations of many-particle limits
Department of Mathematical sciences, University of Bath, Claverton
BA2 7AY, United
2 ICMS and Dep. of Math. and Comp. Sciences, TU Eindhoven, Den Dolech 2, 5612 AZ Eindhoven, the Netherlands
Revised: 4 January 2013
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.
Mathematics Subject Classification: 35A15 / 5Q84
Key words: Wasserstein / gradient flows / Fokker–Planck / Gamma-convergence / large deviations
© EDP Sciences, SMAI, 2013
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