{
  "abstract": "We study the eigenvalues of the random Laplacian matrix $D - A$, where $A$ is a Wigner matrix with sub-Gaussian entries and the diagonal matrix $D$ contains the row sums of $A$. Our main results show that the extreme eigenvalues of this model exhibit Poisson statistics; in particular, after the appropriate centering and scaling, the largest eigenvalue converges to the Gumbel distribution as the dimension of the matrix tends to infinity. This confirms, for general sub-Gaussian entries, a phenomenon the authors previously established only in the Gaussian case [Electron. J. Probab. 30 (2025), Paper No. 104], resolving a conjecture raised there. As a corollary, for an Erdős--Rényi random graph, we show the asymptotic fluctuations of the algebraic connectivity (Fiedler value) can be described in terms of the Gumbel distribution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09076",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrew Campbell"
    },
    {
      "name": "Kyle Luh"
    },
    {
      "name": "Sean O'Rourke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/75wnssgnm362r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09076",
  "fulltext_url": null,
  "id": "75wnssgnm362r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09076",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7221018941",
  "pdf_url": "https://arxiv.org/pdf/2610.09076",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/75wnssgnm362r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09076",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09076"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Universality for the extreme eigenvalues of Laplacian random matrices",
  "title_text": "Universality for the extreme eigenvalues of Laplacian random matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/75wnssgnm362r",
  "venue": "arXiv",
  "versions": []
}