{
  "abstract": "We consider $N \\times N$ random band matrices $H = (H_{xy})$ with centered complex Gaussian entries, indexed by points $x,y$ on the two-dimensional discrete torus $(\\mathbb{Z} / \\sqrt{N} \\mathbb{Z})^2$. The matrix entries $H_{xy}$ vanish whenever the distance between $x$ and $y$ exceeds a constant multiple of the bandwidth parameter $W$. We prove that, for any fixed $\\varepsilon>0$, if $W\\geq(\\log N)^{2+\\varepsilon}$, then all bulk eigenvectors are delocalized with high probability. Equivalently, this yields a lower bound of order $\\exp(W^{1/2-\\varepsilon})$ on the localization length of two-dimensional random band matrices for arbitrarily small constant $\\varepsilon>0$, improving the superpolynomial lower bound $W^C$ for every fixed constant $C>0$ established in arXiv:2503.07606. A key ingredient of our proof is a new strategy that closes the resolvent flow analysis using only loop observables of order at most two, without relying on the higher-order loop hierarchy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24426",
  "author_total": 2,
  "authors": [
    {
      "name": "Xujie Lai"
    },
    {
      "name": "Fan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c209cbkzr7wbz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24426",
  "fulltext_url": null,
  "id": "c209cbkzr7wbz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24426",
  "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"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7214031335",
  "pdf_url": "https://arxiv.org/pdf/2609.24426",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c209cbkzr7wbz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2609.24426",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24426"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Localization Lengths for Two-Dimensional Random Band Matrices: Stretched-Exponential Lower Bounds",
  "title_text": "Localization Lengths for Two-Dimensional Random Band Matrices: Stretched-Exponential Lower Bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/c209cbkzr7wbz",
  "venue": "arXiv",
  "versions": []
}