{
  "abstract": "We develop Stein's method, with explicit constants throughout, for the discrete Bessel distribution: the law of a Poisson variable given its difference from an independent Poisson variable. The Bessel family is characterized by a birth-death operator with quadratic death rate $n(n+k)$ and as the exact fixed-point set of a centered quadratic-bias transform, and we prove a dependency expansion of Arratia-Goldstein-Gordon type: two joint moments of a column array control the total-variation distance from the conditioned row sum to a matched Bessel law. Applied to the row-constrained Fisher-Yates ensemble on $2\\times c$ contingency tables -- independent Bernoulli or capped-Poisson entries conditioned on the row-sum difference, column sums free -- this yields a limit theorem -- which upgrades to the entire conditioned table at the same two-moment error -- a completely explicit enumeration estimate, and an exact divide-and-conquer sampler with certified acceptance. The entire apparatus -- operator, expansion, enumeration, sampler -- generalizes to $r\\times c$ tables, where conditioning on all successive row differences produces a hyper-Bessel law. Verification scripts are included as ancillary files.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00263",
  "author_total": 1,
  "authors": [
    {
      "name": "Stephen DeSalvo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ay9gp0shqf39n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00263",
  "fulltext_url": null,
  "id": "ay9gp0shqf39n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00263",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00263",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ay9gp0shqf39n.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00263",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00263"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Two moments suffice for Bessel approximation: conditioned differences, contingency tables, and probabilistic divide-and-conquer",
  "title_text": "Two moments suffice for Bessel approximation: conditioned differences, contingency tables, and probabilistic divide-and-conquer",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/ay9gp0shqf39n",
  "venue": "arXiv",
  "versions": []
}