{
  "abstract": "We show that the overlaps of two independent replicas drawn from the Gibbs measure of the Curie--Weiss model with random field (CWRF) exhibit sub-Gaussian tails when the inverse temperature $ β< 1$ and the random field is drawn from a Gaussian distribution that makes the expected magnetization of the CWRF equal to its expected overlap in the thermodynamic limit. To show this, we prove finite-moment concentration via a rigorous Laplace approximation for a certain random rate function, and ``bootstrap'' it to a uniform bound for the moment-generating function of the squared overlap deviations using a sharp analysis of the associated rate function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08169",
  "author_total": 3,
  "authors": [
    {
      "name": "Yutong Li"
    },
    {
      "name": "Juspreet Singh Sandhu"
    },
    {
      "name": "Jonathan Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c3tbv6np456g3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08169",
  "fulltext_url": null,
  "id": "c3tbv6np456g3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08169",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
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  ],
  "openalex": "W7212029059",
  "pdf_url": "https://arxiv.org/pdf/2609.08169",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c3tbv6np456g3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:49Z",
      "native_id": "2609.08169",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08169"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On overlap concentration in the Curie-Weiss Random Field model",
  "title_text": "On overlap concentration in the Curie-Weiss Random Field model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/c3tbv6np456g3",
  "venue": "arXiv",
  "versions": []
}