{
  "abstract": "We consider the classical Maki--Thompson rumour model with $n$ initially ignorant individuals and one initial spreader. The final number of ignorants, divided by $n$, is known to satisfy the law of large numbers, the central limit theorem and the large deviation principle. We establish a moderate deviation principle for fluctuations of this proportion of order $b_n/\\sqrt n$, where $b_n\\to\\infty$ and $b_n^2=o(\\log n)$. The proof rests on the exact final-size distribution, sharp asymptotics for the associated automata numbers, and a uniform point probability expansion at the moderate deviation scale. Numerical comparisons of both tails illustrate the intermediate scale and the effect of early extinction on upper tail probabilities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.08629",
  "author_total": 2,
  "authors": [
    {
      "name": "Shaochen Wang"
    },
    {
      "name": "Guangyu Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1bdcsqe9rkpv4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.08629",
  "fulltext_url": null,
  "id": "1bdcsqe9rkpv4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.08629",
  "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": "W7160900670",
  "pdf_url": "https://arxiv.org/pdf/2605.08629",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1bdcsqe9rkpv4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2605.08629",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.08629"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Moderate deviations for the Maki--Thompson rumour model",
  "title_text": "Moderate deviations for the Maki--Thompson rumour model",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1bdcsqe9rkpv4",
  "venue": "arXiv",
  "versions": []
}