{
  "abstract": "Let $π_n$ be a uniform parking function of size $n$. We determine the scale at which its first $k$ coordinates cease to be close in total variation to $k$ independent uniform variables on $\\{1,\\ldots,n\\}$. The distance is comparable to $1\\wedge \\sqrt{k\\log(k+1)/n}$, uniformly for $n\\ge2$ and $1\\le k\\le n$, and tends to one above the scale $n/\\log n$. At the critical scale $k\\simλn/\\log n$, it converges to $2Φ(\\sqrt{λ/π})-1$, where $Φ$ is the standard normal distribution function. A key ingredient is the Lorentzian property of the occupation generating polynomial of parking functions. Together with a strengthened Han inequality, this yields a relative entropy estimate for approximation by the product of the one-coordinate marginals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40082",
  "author_total": 1,
  "authors": [
    {
      "name": "Igor Kortchemski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agxpvwdtdtezr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40082",
  "fulltext_url": null,
  "id": "agxpvwdtdtezr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40082",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40082",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agxpvwdtdtezr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40082",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40082"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A total variation threshold for the first coordinates of uniform parking functions via Lorentzian polynomials",
  "title_text": "A total variation threshold for the first coordinates of uniform parking functions via Lorentzian polynomials",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/agxpvwdtdtezr",
  "venue": "arXiv",
  "versions": []
}