{
  "abstract": "We study discrete-time $N$-dimensional mean-field systems on the torus subject to additive noise whose probability density is bounded away from zero. Given a Lipschitz one-particle map and interaction term, we prove that, if the lower bound on the noise density is sufficiently large, the $N$-dimensional transfer operator $\\mathcal P_N$ preserves a dimension-independent class of sub-Gaussian probability measures. Moreover, $\\mathcal P_N$ is a one-step contraction in the Dobrushin-Wasserstein distance and therefore admits a unique invariant measure $ρ_N$, which is itself sub-Gaussian. Under the same condition on the noise strength, we show that the associated self-consistent transfer operator is a one-step contraction in Wasserstein distance and hence admits a unique fixed point $ρ$. We further prove, using these contraction estimates, that $\\mathcal P_N$ preserves an $O(N^{-1/2})$ neighbourhood of the product measure $ρ^{\\otimes N}$ in the Dobrushin-Wasserstein metric, and in particular that $ρ_N$ belongs to this neighbourhood. Finally, we establish uniform-in-time propagation of chaos in the Dobrushin-Wasserstein metric and, under the additional assumption that the noise density is of bounded variation, in total variation for every fixed-dimensional marginal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05769",
  "author_total": 2,
  "authors": [
    {
      "name": "Giuseppe Tenaglia"
    },
    {
      "name": "Matteo Tanzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9sm159msx3mbf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05769",
  "fulltext_url": null,
  "id": "9sm159msx3mbf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05769",
  "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.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7212011701",
  "pdf_url": "https://arxiv.org/pdf/2609.05769",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9sm159msx3mbf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05769",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05769"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Uniform in time propagation of chaos for noisy mean-field coupled maps",
  "title_text": "Uniform in time propagation of chaos for noisy mean-field coupled maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/9sm159msx3mbf",
  "venue": "arXiv",
  "versions": []
}