{
  "abstract": "We study the overhand shuffle with a fixed cut probability $p\\in(0,1)$. In the packet-reversal convention, each gap is cut independently with probability $p$, and each resulting packet is reversed in place. We prove total-variation cutoff at \\[ \\frac{p^2}{2(1-p)π^2}\\,n^2\\log n. \\] The lower bound uses an exact finite-deck cosine eigenfunction and a uniform conditional-variance estimate. For the upper bound, a coalescing coupling reduces a transposition discrepancy to a symmetric killed two-card chain. Its principal decay rate is $(1-p)π^2/(p^2n^2)+o(n^{-2})$. A boundary-flux identity bounds the sum of adjacent discrepancy probabilities without a factor equal to the deck size. The remaining ingredient is a two-sided $L^1$ inequality on permutations, with constant at most $\\sqrt n\\exp\\{O(\\sqrt{\\log n\\log\\log(n+2)})\\}$. Its proof decomposes a fixed block-table fiber into assignment words and independent smaller permutations, and closes a recursion using a multivariate hypergeometric inequality and an explicit routing comparison. We also prove relative-entropy cutoff with an $O_p(n^2)$ window about the intrinsic entropy transition time. Its leading coefficient lies between the total-variation coefficient and twice that value; a sharp entropy location is not obtained. The proof states the normalization and hypotheses of its established functional-inequality inputs. An appendix proves the intermediate static bounds and explains the change from one-scale averaging to recursive fibers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00137",
  "author_total": 1,
  "authors": [
    {
      "name": "Yunjiang Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9d9r47ma3b6tr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00137",
  "fulltext_url": null,
  "id": "9d9r47ma3b6tr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00137",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7216512908",
  "pdf_url": "https://arxiv.org/pdf/2610.00137",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9d9r47ma3b6tr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00137",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00137"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Cutoff for the Overhand Shuffle",
  "title_text": "Cutoff for the Overhand Shuffle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/9d9r47ma3b6tr",
  "venue": "arXiv",
  "versions": []
}