{
  "abstract": "We investigate the longest increasing subsequences (LIS) of random permutations distributed under the Luce model with weights $\\theta_1^{(n)} \\ge \\ldots \\ge \\theta_n^{(n)}$. Our first main result provides a general formula for the growth rate of the LIS. For example, we get that the LIS of Luce permutations with Sukhatme weights $\\theta_k^{(n)} = n-k+1$ grows like $\\sqrt{n}$. We also give simple conditions for the LIS to be of order $n^\\beta$, for any given $\\beta\\in[1/2,1)$. Our second main result states that, if the weights are of the form $\\theta_k^{(n)} = f\\big( (k-1)/n \\big)$ for a sufficiently regular function $f$, then the LIS divided by $2\\sqrt{n}$ converges in probability to a constant $K(f)$ described by a variational problem. Throughout, we make extensive use of coupling techniques; in particular, to prove our second main result, we argue that Luce random permutations behave similarly to random permutations sampled from the ``Luce permuton''.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30382",
  "author_total": 2,
  "authors": [
    {
      "name": "Jacopo Borga"
    },
    {
      "name": "Victor Dubach"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brdna2eqkma1m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30382",
  "fulltext_url": null,
  "id": "brdna2eqkma1m",
  "issns": [],
  "landing_url": "https://hal.science/hal-05837644v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223292703",
  "pdf_url": "https://hal.science/hal-05837644/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brdna2eqkma1m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05837644",
      "source": "hal",
      "url": "https://hal.science/hal-05837644v1"
    },
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.30382",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30382"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The longest increasing subsequences of Luce permutations and permutons",
  "title_text": "The longest increasing subsequences of Luce permutations and permutons",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/brdna2eqkma1m",
  "venue": "HAL",
  "versions": []
}