{
  "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",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06343",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohamed Alfaki Aboubacrine Assadek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d2na53cdbrzak.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06343",
  "fulltext_url": null,
  "id": "d2na53cdbrzak",
  "issns": [],
  "landing_url": "https://univ-angers.hal.science/hal-05774768v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "hal",
      "1.math.math-fa"
    ],
    [
      "hal",
      "1.math.math-mp"
    ],
    [
      "hal",
      "1.math.math-pr"
    ],
    [
      "hal",
      "1.math.math-sp"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7220700818",
  "pdf_url": "https://univ-angers.hal.science/hal-05774768/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d2na53cdbrzak.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:46Z",
      "native_id": "hal-05774768",
      "source": "hal",
      "url": "https://univ-angers.hal.science/hal-05774768v1"
    },
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.06343",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06343"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mp",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A CONSTRAINED WASSERSTEIN GRADIENT FLOW FOR MEAN-FIELD LANGEVIN DYNAMICS",
  "title_text": "A CONSTRAINED WASSERSTEIN GRADIENT FLOW FOR MEAN-FIELD LANGEVIN DYNAMICS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/d2na53cdbrzak",
  "venue": "HAL",
  "versions": []
}