{
  "abstract": "We study the local density-dependent diffusion $dY_t=-Ξ(p_t(Y_t))\\nablaΦ(Y_t)\\,dt+\\sqrt2\\,dW_t$ and a clipped, randomly shifted histogram particle approximation on $\\mathbb{R}^d$. The central difficulty is that the empirical density is evaluated at the particles' locations and re-enters their drift, while the confining force $\\nablaΦ$ may be unbounded. We provide a path-space entropy proof under two verifiable analytic conditions: a uniform pointwise Gaussian envelope for the true density $p_t$, and a Gaussian--polynomial bound for its spatial gradient $\\nabla p_t$. The potential is allowed to have a gradient of at most linear growth. The probabilistic input is a weighted exponential occupancy estimate under the independent product law. It is proved by Poissonizing the system at total intensity $N-1$, performing a one-cell leave-one-out estimate bounded via Poisson information, using Gaussian cell summability, and de-Poissonizing. For every fixed time horizon $T$, we obtain $\\operatorname{Ent}(P_t^{N,k}|p_t^{\\otimes k})\\leq C_T k(h^2(1+|\\log h|)+(h^{-d}+\\log N)/N)$. Consequently, selecting the optimally balanced bandwidth $h\\asymp (N\\log N)^{-1/(d+2)}$ yields a total variation error of $\\Vert P_t^{N,k}-p_t^{\\otimes k}\\Vert_{\\operatorname{TV}}\\leq C_T\\sqrt{k}\\,N^{-1/(d+2)}(\\log N)^{d/[2(d+2)]}$ for fixed $k$. This includes the usual Ornstein--Uhlenbeck density and the density-dependent OU model whenever the PDE estimates hold on the considered interval. Furthermore, the histogram estimator offers a scalable approach for particle approximations. Using occupied-cell hashing, one algorithm step evaluates in expected $O(dLN)$ operations under standard constant-time hashing assumptions. For a fixed dimension and number of shifts, this requires expected $O(N)$ time, avoiding the $O(N^2)$ evaluation cost typical of standard kernel density estimators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.19583",
  "author_total": 2,
  "authors": [
    {
      "name": "Denis Belomestny"
    },
    {
      "name": "Ekaterina Morozova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fdt7bk0df018d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.19583",
  "fulltext_url": null,
  "id": "fdt7bk0df018d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.19583",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7170149856",
  "pdf_url": "https://arxiv.org/pdf/2607.19583",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fdt7bk0df018d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2607.19583",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.19583"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Density-Dependent McKean--Vlasov Diffusions: Subgaussian Occupancy Bounds and Polynomial Propagation of Chaos",
  "title_text": "Density-Dependent McKean--Vlasov Diffusions: Subgaussian Occupancy Bounds and Polynomial Propagation of Chaos",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/fdt7bk0df018d",
  "venue": "arXiv",
  "versions": []
}