{
  "abstract": "Let $A$ be the (non-symmetric) adjacency matrix of a uniformly random $d$-regular directed graph on $n$ vertices, and let $Ξ$ be independent of $A$ with i.i.d. Rademacher entries. Suppose that $\\min(d,n-d)\\geλn$ for some fixed $λ\\in(0,1/2]$. We show that there exists $c > 0$, depending only on $λ$, such that \\[ \\mathbf P_{A,Ξ}\\{\\operatorname{rank}(A\\circΞ)\\le n-k\\}\\le e^{-c nk},\\qquad 1\\le k\\le n. \\] As an ingredient in the proof of the rank bound, we use the case $κ=0$ of the following quantitative smallest singular value estimate: \\[ \\mathbf P_{A,Ξ}\\{s_n(A\\circΞ)\\leκ\\} \\le Cκ\\sqrt n+e^{-c' n}, \\qquad κ\\ge0, \\] where $C,c'>0$ depend only on $λ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05938",
  "author_total": 4,
  "authors": [
    {
      "name": "Huaijin Liang"
    },
    {
      "name": "Yuxiao Shi"
    },
    {
      "name": "Kexin Yu"
    },
    {
      "name": "Tingzhou Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a9tmm0ec7dekw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05938",
  "fulltext_url": null,
  "id": "a9tmm0ec7dekw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05938",
  "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": "W7220702634",
  "pdf_url": "https://arxiv.org/pdf/2610.05938",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a9tmm0ec7dekw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05938",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05938"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Rank and Invertibility of Dense Signed Random Regular Matrices",
  "title_text": "Rank and Invertibility of Dense Signed Random Regular Matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/a9tmm0ec7dekw",
  "venue": "arXiv",
  "versions": []
}