{
  "abstract": "We study increasing propagation of chaos for the critical Curie- Weiss model (i.e. the mean-field Ising model at critical inverse temperature 1, with no external field). We give a simple way to see that for windows of size k(N) of smaller order than sqrt{N} we still have propagation of chaos (reproving earlier results, see e.g.[1]), while for k(N) of order sqrt{N} the propagation of chaos breaks down. The law of a single spin converges to π, the Bernoulli law with parameter 1/2. If k(N) = alpha sqrt{N}, we give an explicit formula for the limiting distance in total variation of the law of the first k(N) spins with respect to the k-fold product of pi, as a function of alpha. For even larger window sizes, the distribution of the spins has, in the thermodynamical limit, maximal distance to the k-fold product of pi. One of the ingredients of the proof is a result about the unimodality/non- unimodality of the law of the number of positive spins among the first k = k(N) spins, which may be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02464",
  "author_total": 3,
  "authors": [
    {
      "name": "Nina Gantert"
    },
    {
      "name": "Matthias Löwe"
    },
    {
      "name": "Kilian Schnappinger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/213q4zqcnqd59.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02464",
  "fulltext_url": null,
  "id": "213q4zqcnqd59",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02464",
  "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": "W7207547390",
  "pdf_url": "https://arxiv.org/pdf/2609.02464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/213q4zqcnqd59.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02464"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "When does propagation of chaos in the critical Curie-Weiss model stop?",
  "title_text": "When does propagation of chaos in the critical Curie-Weiss model stop?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/213q4zqcnqd59",
  "venue": "arXiv",
  "versions": []
}