{
  "abstract": "In this paper, we prove universality of the distribution of the cokernels of random $p$-adic matrices with inhomogeneously balanced columns. More precisely, let $u \\ge 0$ be an integer, and for each positive integer $n$, let $A(n)$ be a random $n \\times (n+u)$ matrix over $\\mathbb{Z}_p$ whose $i$-th column is $α_n(i)$-balanced. We prove that if $\\sum_{i=1}^{n+u} \\exp(-εα_n(i)n) \\to 0$ as $n \\to \\infty$ for every $ε>0$, then the cokernels of $A(n)$ converge in distribution, as $n \\to \\infty$, to the same limiting law as the cokernels of Haar-random $n \\times (n+u)$ matrices over $\\mathbb{Z}_p$. This extends a universality theorem of Nguyen and Wood to random $p$-adic matrices with inhomogeneously balanced columns.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.02180",
  "author_total": 2,
  "authors": [
    {
      "name": "Jungin Lee"
    },
    {
      "name": "Sungjin Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ckwcmhn4cwqpy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.02180",
  "fulltext_url": null,
  "id": "ckwcmhn4cwqpy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.02180",
  "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.NT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7163210161",
  "pdf_url": "https://arxiv.org/pdf/2606.02180",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ckwcmhn4cwqpy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2606.02180",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.02180"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Universality of the cokernels of random $p$-adic matrices with inhomogeneously balanced columns",
  "title_text": "Universality of the cokernels of random p-adic matrices with inhomogeneously balanced columns",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/ckwcmhn4cwqpy",
  "venue": "arXiv",
  "versions": []
}