{
  "abstract": "Let $X_1,\\ldots,X_n$ be almost surely distinct independent real-valued random variables. Let $σ$ be the random permutation of $\\{1,\\ldots,n\\}$ such that $X_{σ(1)}<X_{σ(2)}<\\cdots< X_{σ(n)}$. We show that the set of laws of $σ$, as the laws of $X_1,\\ldots,X_n$ vary, has semialgebraic dimension \\[ \\sum_{k=2}^n {n \\choose k}(k-1)! \\] as a subset of the $(n!-1)$-simplex. This establishes a conjecture of Babson, Duchin, Iseli, Poggi-Corradini, Thurston, and Tucker-Foltz who proved that the dimension is upper bounded by the above expression. We prove their conjecture by constructing a family of finitely supported laws for $X_1,\\ldots,X_n$ that provides the correct dimension. We also give an alternative proof of the upper bound using a theorem of Radford. Furthermore, we show that the Mallows law on permutations cannot arise as a law of $σ$ for $n\\geq 4$, answering a question of Ed Crane.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11895",
  "author_total": 1,
  "authors": [
    {
      "name": "Luke Turvey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85kcrrep0m2vz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11895",
  "fulltext_url": null,
  "id": "85kcrrep0m2vz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11895",
  "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.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7221189103",
  "pdf_url": "https://arxiv.org/pdf/2610.11895",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/85kcrrep0m2vz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11895",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11895"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Permutations from ranking independent random variables",
  "title_text": "Permutations from ranking independent random variables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/85kcrrep0m2vz",
  "venue": "arXiv",
  "versions": []
}