{
  "abstract": "Fix $b\\in(0,1)$, let $1\\leq k\\leq n$, and let $A=(A_{ij})$ be an $n\\times n$ random matrix with independent real entries satisfying $$ \\sup_{x\\in\\mathbb{R}}\\mathbb{P}\\{A_{ij}=x\\}\\leq b<1 \\qquad (1\\leq i,j\\leq n). $$ We show that there exists $c>0$ such that $$ \\mathbb{P}\\{\\operatorname{rank} A\\leq n-k\\}\\leq \\exp(-cnk), \\qquad 1\\leq k\\leq n. $$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.25204",
  "author_total": 1,
  "authors": [
    {
      "name": "Achintya Raya Polavarapu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ej9m39x3yzkv2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.25204",
  "fulltext_url": null,
  "id": "ej9m39x3yzkv2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.25204",
  "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": "W7165960217",
  "pdf_url": "https://arxiv.org/pdf/2606.25204",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ej9m39x3yzkv2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2606.25204",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.25204"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Exponential Rank Bounds for Random Matrices",
  "title_text": "Exponential Rank Bounds for Random Matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/ej9m39x3yzkv2",
  "venue": "arXiv",
  "versions": []
}