{
  "abstract": "Let $n=2^d$. We prove that the worst-start total-variation mixing time of the full labelled Thorp shuffle satisfies, for every fixed $0<\\varepsilon<1$, \\[ t_{\\mathrm{mix}}(\\varepsilon) \\le C_* d^{5/3}+O_\\varepsilon\\!\\left(d^{4/3}\\log(d+2)\\right), \\qquad C_*=5.1536951454\\ldots . \\] Time is measured in ordinary Thorp shuffles. This improves the previously published full-deck upper bound $O(d^3)$ of Morris. The geometric starting point is elementary: label the $n=2^d$ positions by binary strings. One physical Thorp shuffle is a random swap layer on one coordinate matching of the $d$-dimensional cube, followed by a deterministic cyclic rotation of the coordinates. In a rotating frame that deterministic rotation disappears, so $d$ successive physical shuffles become one \\emph{sweep}: one independent random swap layer in each coordinate direction. The proof then combines five ingredients. First, a collision-graph representation and negative dependence give pointwise smoothing for ordered marked cards. Second, an entropy argument is sharpened by moving an endpoint moment up to the critical exponent $β_c=\\log_2(3/2)$, yielding an entropy-preparation clock $s^2/(2\\log(3/2))+O(s\\log s)$. Third, exact multiplicities in the ordered $h$-tuple permutation representation amplify marked-card bounds into Fourier operator and energy estimates on low representation levels. Fourth, entropy truncation produces a positive mixture whose regular component retains the marked-card budget. Finally, only two long blocks need this entropy regularization: a shorter third block is used solely for additional low-level smoothing. Optimizing the three block lengths gives the constant above.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18884",
  "author_total": 1,
  "authors": [
    {
      "name": "Yunjiang Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/513175m4wfq3f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18884",
  "fulltext_url": null,
  "id": "513175m4wfq3f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18884",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7222026277",
  "pdf_url": "https://arxiv.org/pdf/2610.18884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/513175m4wfq3f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.18884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18884"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A subquadratic upper bound for the mixing time of the Thorp shuffle",
  "title_text": "A subquadratic upper bound for the mixing time of the Thorp shuffle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/513175m4wfq3f",
  "venue": "arXiv",
  "versions": []
}