{
  "abstract": "We study finite-rank deformations of inhomogeneous random symmetric/Hermitian matrices $H_N=(σ_{ij}W_{ij})_{i,j=1}^N$, whose variance profile satisfies $\\sum_jσ_{ij}^2=1$. Writing $σ_N^*=\\max_{i,j}σ_{ij}$ for the matrix sparsity parameter, we establish the BBP transition of outlier eigenvalues at the level of the law of large numbers in two regimes of moment conditions on $\\{W_{ij}\\}$: (1) under a uniform sub-Weibull bound with exponent $0<α\\le 2$ and the sharp assumption $σ_N^*(\\log N)^{1/α}\\to 0$, the convergence holds almost surely; (2) under uniformly integrable $p$-th powers for some $p\\ge 4$ and the sharp assumption $N(σ_N^*)^{p-2}=O(1)$, the convergence holds in probability. Our approach combines sharp norm estimates, fixed-degree polynomial isotropic laws, and a finite-dimensional resolvent equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24796",
  "author_total": 4,
  "authors": [
    {
      "name": "Ruohan Geng"
    },
    {
      "name": "Zhantao He"
    },
    {
      "name": "Dang-Zheng Liu"
    },
    {
      "name": "Guangyi Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/50wrpt6r7q0th.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24796",
  "fulltext_url": null,
  "id": "50wrpt6r7q0th",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24796",
  "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.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7223033837",
  "pdf_url": "https://arxiv.org/pdf/2610.24796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/50wrpt6r7q0th.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24796"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "BBP Transition for Deformed Inhomogeneous Random Matrices",
  "title_text": "BBP Transition for Deformed Inhomogeneous Random Matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/50wrpt6r7q0th",
  "venue": "arXiv",
  "versions": []
}