A CONSTRAINED WASSERSTEIN GRADIENT FLOW FOR MEAN-FIELD LANGEVIN DYNAMICS
Abstract
In the continuity of [1, 2, 3], we study a class of constrained mean-field Langevin dynamics formulated as a Wasserstein gradient flow with an energy constraint. We show that the constrained evolution therefore defines a well-posed dissipative dynamics in the Wasserstein space P2(Rd). We prove that the flow preserves probability mass and the energy constraint, dissipates the free energy monotonically, and converges exponentially to a unique constrained equilibrium under geodesic convexity assumptions. Using synchronous coupling, under Lipschitz assumptions, we demonstrate the quantitative L2 -propagation of chaos with a Fournier-Guillin bound, and under conditions of sufficient dissipativity, we derive an explicit time-uniform bound. We also demonstrate exponential controls in the W2 Wasserstein metric and the contraction of the invariant measure map. Using log-Sobolev inequalities, we show that the mean-field entropies decay exponentially along the constrained flow. The results are applied to several concrete and original examples. Keywords and phrases: Wasserstein gradient flows • mean-field Langevin dynamics • constrained nonlinear Fokker-Planck equations • Lagrange multiplier • JKO scheme • propagation of chaos • synchronous coupling • exponential ergodicity • functional inequality • log-Sobolev inequality • Transport inequality • Talagrand T2 -inequality
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BibTeX
@misc{assadek2026constrained,
title = {{A CONSTRAINED WASSERSTEIN GRADIENT FLOW FOR MEAN-FIELD LANGEVIN DYNAMICS}},
author = {Mohamed Alfaki Aboubacrine Assadek},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06343},
eprint = {2610.06343},
archivePrefix = {arXiv},
url = {https://univ-angers.hal.science/hal-05774768v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A CONSTRAINED WASSERSTEIN GRADIENT FLOW FOR MEAN-FIELD LANGEVIN DYNAMICS
AU - Mohamed Alfaki Aboubacrine Assadek
PY - 2026
DA - 2026/10/02
PB - HAL
DO - 10.48550/arxiv.2610.06343
UR - https://univ-angers.hal.science/hal-05774768v1
AB - In the continuity of [1, 2, 3], we study a class of constrained mean-field Langevin dynamics formulated as a Wasserstein gradient flow with an energy constraint. We show that the constrained evolution therefore defines a well-posed dissipative dynamics in the Wasserstein space P2(Rd). We prove that the flow preserves probability mass and the energy constraint, dissipates the free energy monotonically, and converges exponentially to a unique constrained equilibrium under geodesic convexity assumptions. Using synchronous coupling, under Lipschitz assumptions, we demonstrate the quantitative L2 -propagation of chaos with a Fournier-Guillin bound, and under conditions of sufficient dissipativity, we derive an explicit time-uniform bound. We also demonstrate exponential controls in the W2 Wasserstein metric and the contraction of the invariant measure map. Using log-Sobolev inequalities, we show that the mean-field entropies decay exponentially along the constrained flow. The results are applied to several concrete and original examples. Keywords and phrases: Wasserstein gradient flows • mean-field Langevin dynamics • constrained nonlinear Fokker-Planck equations • Lagrange multiplier • JKO scheme • propagation of chaos • synchronous coupling • exponential ergodicity • functional inequality • log-Sobolev inequality • Transport inequality • Talagrand T2 -inequality
ER -