# Wasserstein gradient flows from large deviations of many-particle limits

Manh Hong Duong; Vaios Laschos; Michiel Renger

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 4, page 1166-1188
- ISSN: 1292-8119

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topDuong, Manh Hong, Laschos, Vaios, and Renger, Michiel. "Wasserstein gradient flows from large deviations of many-particle limits." ESAIM: Control, Optimisation and Calculus of Variations 19.4 (2013): 1166-1188. <http://eudml.org/doc/272768>.

@article{Duong2013,

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.},

author = {Duong, Manh Hong, Laschos, Vaios, Renger, Michiel},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Wasserstein; gradient flows; Fokker–Planck; gamma-convergence; large deviations; path-space rate functional; Wasserstein gradient discretization scheme},

language = {eng},

number = {4},

pages = {1166-1188},

publisher = {EDP-Sciences},

title = {Wasserstein gradient flows from large deviations of many-particle limits},

url = {http://eudml.org/doc/272768},

volume = {19},

year = {2013},

}

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

PB - EDP-Sciences

VL - 19

IS - 4

SP - 1166

EP - 1188

AB - 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.

LA - eng

KW - Wasserstein; gradient flows; Fokker–Planck; gamma-convergence; large deviations; path-space rate functional; Wasserstein gradient discretization scheme

UR - http://eudml.org/doc/272768

ER -

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