{
  "abstract": "We establish a quantitative local law for random $N$-lifts of a fixed finite connected simple graph with minimum degree at least three. Away from the singular energies of the universal-cover spectrum, we obtain high-probability entrywise Green's function estimates down to spectral scales $(\\log N)^C/N$, uniformly in the bulk and near regular edges and cusps. As a consequence, we establish complete eigenvector delocalization: every normalized eigenvector $u$ whose eigenvalue stays a small but fixed positive distance away from the singular energies satisfies $\\|u\\|_\\infty\\leq(\\log N)^C/\\sqrt{N}$ with high probability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37463",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiaoyang Huang"
    },
    {
      "name": "Ruizhe Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fk4qnkybbc5cd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37463",
  "fulltext_url": null,
  "id": "fk4qnkybbc5cd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37463",
  "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-ph"
    ],
    [
      "arxiv",
      "math.CO"
    ],
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      "arxiv",
      "math.MP"
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      "arxiv",
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      "arxiv",
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    [
      "openalex",
      "2613|Random Matrices and Applications"
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  "openalex": "W7224102136",
  "pdf_url": "https://arxiv.org/pdf/2610.37463",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fk4qnkybbc5cd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.37463",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37463"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "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": "Local Law and Eigenvector Delocalization for Random Lifts",
  "title_text": "Local Law and Eigenvector Delocalization for Random Lifts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/fk4qnkybbc5cd",
  "venue": "arXiv",
  "versions": []
}