{
  "abstract": "We consider bipartite Erdős-Rényi graphs $\\mathbb{G}(n, p, d/\\sqrt{np})$ with two parts of sizes $n$ and $p$, respectively, and edge probability $d/\\sqrt{pn}$. We show that for $d > b_* \\log (n+p)$ all eigenvectors of its adjacency matrix, with eigenvalues away from zero, are delocalized with high probability. The threshold $b_*$ is an explicit function of the size ratio $n/p$ and optimal for eigenvector delocalization near the spectral edges. Our results extend to bulk eigenvectors down to the optimal threshold $d\\geq \\mathcal{D}\\sqrt{\\log (n+p)}$ for a constant $\\mathcal D \\geq 1$. In the supercritical scale $d \\gg \\log (n+p)$ we show that all eigenvectors are delocalized. Our results also hold for sparse rectangular random matrices with independent entries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42088",
  "author_total": 2,
  "authors": [
    {
      "name": "Johannes Alt"
    },
    {
      "name": "Serafina Wald"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/32srbtj4crv13.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42088",
  "fulltext_url": null,
  "id": "32srbtj4crv13",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42088",
  "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-ph"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.42088",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/32srbtj4crv13.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2610.42088",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42088"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Delocalized region of bipartite Erdős-Rényi graphs",
  "title_text": "Delocalized region of bipartite Erdős-Rényi graphs",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/32srbtj4crv13",
  "venue": "arXiv",
  "versions": []
}