{
  "abstract": "Consider an $N\\times N$ random band matrix $H$ with bandwidth $W$ with centered real Gaussian entries. We prove that, under the (almost) sharp assumption $W^2\\ll N/\\log N$, the bulk local statistics of $H$ are asymptotically a Poisson point process. Combined with the bulk universality results from arXiv:2501.01718 and arXiv:2506.06441, this establishes the Poisson-RMT transition of the local statistics of random band matrices, and complements the results about the localization-delocalization transition of the bulk eigenvectors previously established in arXiv:2501.01718 and arXiv:2506.06441, and arXiv:2508.05802. The key technical inputs are: (1) the fractional moment estimates from arXiv:2508.05802; (2) a novel estimate for the density of states, obtained from the local laws in arXiv:2501.01718 and arXiv:2506.06441.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23389",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiaqi Fan"
    },
    {
      "name": "Guangyi Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1tm15sewxrmtd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23389",
  "fulltext_url": null,
  "id": "1tm15sewxrmtd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23389",
  "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.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.SP"
    ],
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      "openalex",
      "2613|Random Matrices and Applications"
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  "openalex": "W7214018457",
  "pdf_url": "https://arxiv.org/pdf/2609.23389",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1tm15sewxrmtd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23389",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23389"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Poisson statistics of one-dimensional random band matrices",
  "title_text": "Poisson statistics of one-dimensional random band matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/1tm15sewxrmtd",
  "venue": "arXiv",
  "versions": []
}