{
  "abstract": "We study the mixing behavior of three q-deformed card shuffles on $\\mathcal{H}_q(S_n)$: the short systematic scan introduced in \\cite{DiaconisRam2000}, the $q$--deformed random--to--random shuffle introduced in \\cite{AxelrodFreedBraunerChiangComminsLang2024}, and the $q$--deformed $k$--star transposition shuffle, whose $q=1$ counterpart was studied in \\cite{ArfaeeNestoridi}. The first two chains were diagonalized in \\cite{DiaconisRam2000} and \\cite{AxelrodFreedBraunerChiangComminsLang2024}, respectively. Here, we diagonalize the $q$--deformed $k$--star transposition shuffle and use the spectra of the three chains to study their mixing behavior. For fixed $q>1$, we prove that all three exhibit total variation and $\\ell^2$ cutoff. For the short systematic scan, these improve both the upper and lower bounds of Diaconis and Ram \\cite{DiaconisRam2000}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13570",
  "author_total": 2,
  "authors": [
    {
      "name": "Samira Arfaee"
    },
    {
      "name": "Bryan Wong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7mq1jb0ng0naq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13570",
  "fulltext_url": null,
  "id": "7mq1jb0ng0naq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13570",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213362286",
  "pdf_url": "https://arxiv.org/pdf/2609.13570",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7mq1jb0ng0naq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13570",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13570"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Cutoff for q-deformed classical card shuffles in the type A Iwahori--Hecke algebra",
  "title_text": "Cutoff for q-deformed classical card shuffles in the type A Iwahori--Hecke algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7mq1jb0ng0naq",
  "venue": "arXiv",
  "versions": []
}