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

Abstract

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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.

How to cite

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Duong, 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 -

References

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