{
  "abstract": "Based on a semigroup approach, we prove quantitative uniform-in-time propagation of chaos for two systems of interacting particles with singular interaction kernels $K$ of type $L^k$, $k>d$, and a contractive Lipschitz confinement force field. First, we consider a system with moderate interaction, which means that the particles interact through the mollified kernel $K\\ast V^N$, for some approximation of identity $V^N = N^{dα} V(N^α\\cdot),\\, α>0$. Assuming that $\\|K\\|_{L^k}$ is sufficiently small, we obtain that for any $\\varepsilon>0$ the uniform-in-time rate is of order $N^{-\\min\\left(α,\\frac12-\\frac{dα}{2}-\\varepsilon\\right)}$, plus an exponentially small in time contribution of the initial condition. Second, for the classical, non-mollified particle system we establish uniform-in-time propagation of chaos with rate $N^{-\\min\\left(α,\\frac12-\\frac{dα}{2}-\\varepsilon\\right)} + \\|K-K\\ast V^N\\|_{L^{k}}$, plus an exponentially small in time contribution of the initial condition. The method relies on the regularity properties of the solution of the associated nonlinear Fokker-Planck equation combined with estimates of the Duhamel formulation of the mollified empirical measure, together with partial Girsanov transforms for the non-mollified system of particles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15852",
  "author_total": 3,
  "authors": [
    {
      "name": "Nicoleta Cazacu"
    },
    {
      "name": "Alexandre Richard"
    },
    {
      "name": "Milica Tomasevic"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/05wwhsscw9kyx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15852",
  "fulltext_url": null,
  "id": "05wwhsscw9kyx",
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  "landing_url": "https://hal.science/hal-05799936v1",
  "language": "en",
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  "licence_source": "article",
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      "math.AP"
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      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7221822710",
  "pdf_url": "https://arxiv.org/pdf/2610.15852",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/05wwhsscw9kyx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:57Z",
      "native_id": "hal-05799936",
      "source": "hal",
      "url": "https://hal.science/hal-05799936v1"
    },
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15852",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15852"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Uniform-in-time propagation of chaos for singular $L^k$ interaction kernels with rates",
  "title_text": "Uniform-in-time propagation of chaos for singular L^k interaction kernels with rates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/05wwhsscw9kyx",
  "venue": "HAL",
  "versions": []
}