{
  "abstract": "We give an exact asymptotic expansion of the occupation probabilities $a(n,k)$ of the harmonic descent chain, introduced by D. Aldous, as $n\\rightarrow\\infty$ with $k\\in\\mathrm{o}(\\sqrt{n})$. In addition, we extend the recent results of Brandenberger et al. by giving a bound on the rate of convergence of sequences defined recursively by $x_n = \\frac{1}{H_{n-1}}\\sum_{i=1}^{n-1}\\frac{x_i}{n-i}$ for more general initial conditions. This result enables the application of an existing central limit theorem, also by Brandenberger et al., to statistics of the critical beta-splitting tree which satisfy our more general initial conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00347",
  "author_total": 1,
  "authors": [
    {
      "name": "Sean P. Svihla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0acy38k2ggvyd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00347",
  "fulltext_url": null,
  "id": "0acy38k2ggvyd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00347",
  "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.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00347",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0acy38k2ggvyd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00347",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00347"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Exact Asymptotics for the Harmonic Descent Chain and Extended Convergence Bounds for Recursive Statistics",
  "title_text": "Exact Asymptotics for the Harmonic Descent Chain and Extended Convergence Bounds for Recursive Statistics",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0acy38k2ggvyd",
  "venue": "arXiv",
  "versions": []
}