{
  "abstract": "The Rudvalis shuffle removes the top card and reinserts it uniformly at random in one of the bottom two positions. Hildebrand proved the classical upper bound $O(n^3\\log n)$, and Wilson later proved the sharp lower coefficient $1/(8π^2)$, establishing the correct order but leaving the leading upper constant, cutoff, and the cutoff profile open. We prove that the full labelled shuffle has total-variation cutoff at \\[ \\frac{n^3\\log n}{8π^2} \\] with a window of order $n^3$. The upper bound is obtained by writing one deterministic rotation of the shuffle as a nonnormal sweep of adjacent averaging projections, comparing that sweep to a weighted interchange generator, and controlling the entire regular-representation heat trace. The key sharp-window ingredients are heat-kernel smoothing through the Octopus Inequality, zero extension of deletion-harmonic ordered-tuple functions, a representation-theoretic multiplicity payment, and a sectorwise entrance estimate that disposes of all large Young-diagram deficits. For the profile, an exact complex one-card eigenfunction yields a deck statistic whose surviving first Fourier mode converges to a Gaussian shift. A matching full-deck $L^2$ bound then shows that this one-dimensional Gaussian likelihood ratio asymptotically exhausts all remaining information, giving the exact total-variation profile.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01597",
  "author_total": 1,
  "authors": [
    {
      "name": "Yunjiang Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d100fc1jyj199.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01597",
  "fulltext_url": null,
  "id": "d100fc1jyj199",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01597",
  "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/2611.01597",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d100fc1jyj199.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01597",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01597"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Cutoff and a Gaussian-shift profile for the Rudvalis shuffle",
  "title_text": "Cutoff and a Gaussian-shift profile for the Rudvalis shuffle",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/d100fc1jyj199",
  "venue": "arXiv",
  "versions": []
}