{
  "abstract": "We study the asymptotic distribution of the number of primitive, closed geodesics on Weil-Petersson random hyperbolic surfaces with genus $g$ and $n(g)$ cusps, under various growth rates of $n(g)$ as $g\\to\\infty$. We prove that the limiting distribution is Poisson with parameter depending explicitly on the limit of $n(g)^2/g$. This work is inspired by that of Mirzakhani and Petri's on closed surfaces and Hide and Thomas when $g$ is fixed. Our proof relies on first order expansions for Weil-Petersson moduli space volumes in the $n(g)/g\\to 0$ regime. We also obtain some new existence results for small Laplacian eigenvalues.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41002",
  "author_total": 2,
  "authors": [
    {
      "name": "Malo Gatignol"
    },
    {
      "name": "Joe Thomas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2dckhaem2rc4k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41002",
  "fulltext_url": null,
  "id": "2dckhaem2rc4k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41002",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41002",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2dckhaem2rc4k.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41002",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41002"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Lengths of closed geodesics on random non-compact hyperbolic surfaces",
  "title_text": "Lengths of closed geodesics on random non-compact hyperbolic surfaces",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/2dckhaem2rc4k",
  "venue": "arXiv",
  "versions": []
}