{
  "abstract": "We study the empirical eigenvalue distribution of a standardized up Laplacian of the Linial-Meshulam model $Y_{q+1}(n, p)$. We first give a definition of a Gaussian--semicircle law: $\\mathcal{N}(0, σ^2)\\boxplus \\operatorname{SC}(sσ^2)$, and give a combinatorial formula of its moments in terms of pairing partitions. In addition to that, we also prove that the limiting empirical eigenvalue distribution of this standardized up Laplacian follows a Gaussian--semicircle law, in the sense of almost surely weak convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31919",
  "author_total": 1,
  "authors": [
    {
      "name": "Rui Dong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vfghhw1pjhpe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31919",
  "fulltext_url": null,
  "id": "2vfghhw1pjhpe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31919",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7214744802",
  "pdf_url": "https://arxiv.org/pdf/2609.31919",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vfghhw1pjhpe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31919",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31919"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Eigenvalue Distribution of the Laplacian on Random Complexes",
  "title_text": "Eigenvalue Distribution of the Laplacian on Random Complexes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/2vfghhw1pjhpe",
  "venue": "arXiv",
  "versions": []
}