{
  "abstract": "We study the nonlocal continuity equation \\[ \\partial_tμ_b =\\operatorname{div}\\!\\left( μ_b\\nabla\\log\\bigl((I-b^2Δ)^{-1}μ_b\\bigr) \\right) \\] on a closed connected Riemannian manifold. For smooth strictly positive initial data, we prove that as $b \\to 0$, its global solution converges to heat flow $μ(t)$ at the sharp, uniform-in-time rate \\[ \\sup_{t\\ge0}\\|μ_b(t)-μ(t)\\|_{L^1}\\le Cb^2. \\] The key estimate is the uniform dissipation of a $b$-weighted higher-order resolvent energy, which yields exponential relaxation despite the absence of a Wasserstein gradient-flow structure. On the circle, we also analyze the corresponding deterministic $N$-particle dynamics. A weak--strong modulated energy argument gives \\[ \\mathbb E\\!\\left[ \\sup_{t\\ge0}W_1(μ_b^N(t),μ_b(t)) \\right] \\le C(Nb)^{-1/2} \\] for iid initialization. Consequently, the choice $b\\asymp N^{-1/5}$ approximates heat flow uniformly in time at rate $N^{-2/5}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11837",
  "author_total": 4,
  "authors": [
    {
      "name": "Andrea Agazzi"
    },
    {
      "name": "Giuseppe Bruno"
    },
    {
      "name": "Federico Pasqualotto"
    },
    {
      "name": "Philippe Rigollet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/acyk1vvg52myw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11837",
  "fulltext_url": null,
  "id": "acyk1vvg52myw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11837",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212287787",
  "pdf_url": "https://arxiv.org/pdf/2609.11837",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/acyk1vvg52myw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11837",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11837"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Quantitative Diffusive Limits for Singular Nonlocal Transport",
  "title_text": "Quantitative Diffusive Limits for Singular Nonlocal Transport",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:36Z",
  "url": "https://research.draconitic.com/paper/acyk1vvg52myw",
  "venue": "arXiv",
  "versions": []
}