Wasserstein gradient flows from large deviations of many-particle limits

M.H. Duong, V. Laschos, D.R.M. Renger

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)
186 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)1166-1188
Number of pages23
JournalESAIM : Control, Optimisation and Calculus of Variations
Volume19
Issue number4
DOIs
Publication statusPublished - 2013

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