{
  "abstract": "We prove that the spectral gap of a Weil--Petersson random hyperbolic surface of genus $g$ with $n=n(g)\\ge1$ labelled cusps converges in probability to $1/4$ as $g\\to\\infty$, for every sequence $n=o(\\sqrt g)$. More precisely, for each fixed $0<\\varepsilon<1/4$, there are constants $C_\\varepsilon\\ge2$ and $g_\\varepsilon\\ge3$, independent of $n$, such that the expected number of nonzero $L^2$ eigenvalues in $(0,1/4-\\varepsilon]$, counted with multiplicity and including residual eigenvalues, is at most $C_\\varepsilon(n+1)^2/g$ whenever $g\\ge g_\\varepsilon$ and $g\\ge C_\\varepsilon(n+1)^2$. This proves a conjecture of Shen and Wu. A matching lower bound shows that the count estimate is optimal up to constants for each fixed $\\varepsilon$, and that $n=o(\\sqrt g)$ is necessary for convergence of the gap to $1/4$. The proof combines volume estimates uniform in the cusp count with polynomial approximation and a positive trace on truncated surfaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01477",
  "author_total": 1,
  "authors": [
    {
      "name": "Guan Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ah7zbs1aws84j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01477",
  "fulltext_url": null,
  "id": "ah7zbs1aws84j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01477",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01477",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ah7zbs1aws84j.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01477",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01477"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Spectral gaps near one quarter for Weil--Petersson random surfaces with growing cusp number",
  "title_text": "Spectral gaps near one quarter for Weil--Petersson random surfaces with growing cusp number",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/ah7zbs1aws84j",
  "venue": "arXiv",
  "versions": []
}