{
  "abstract": "We study the root-averaged density of states for the Anderson model on the Bethe lattice in the strong-disorder regime. Here the density of states means the root-averaged spectral measure, not a finite-volume eigenvalue counting limit. We assume that the single-site distribution has compact support and has a locally analytic density on an interval $I^\\sharp$ containing a given interval $I$. Combining the random-walk expansion on the tree with a complex-analytic argument for the single-site Stieltjes transforms, we prove that the scaled averaged diagonal resolvent has a holomorphic continuation to a complex neighborhood of $I$ for all sufficiently large $λ$. By the Stieltjes inversion formula, the root-averaged density of states measure is absolutely continuous on the scaled energy window $λI$, and its density is real analytic and has a finite-order strong-disorder expansion there. In the scaled form $E=λξ$, the leading coefficient is the local density of the single-site distribution. All odd coefficients vanish, and the higher coefficients are finite sums determined by occupation profiles of short closed walks on the tree. For the uniform single-site distribution, we compute the first nonzero correction term explicitly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.00478",
  "author_total": 1,
  "authors": [
    {
      "name": "Masahiro Kaminaga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eby7e91s3e5ca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.00478",
  "fulltext_url": null,
  "id": "eby7e91s3e5ca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.00478",
  "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.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7160136366",
  "pdf_url": "https://arxiv.org/pdf/2605.00478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eby7e91s3e5ca.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:55Z",
      "native_id": "2605.00478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.00478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Strong-disorder expansion of the root-averaged density of states for the Anderson model on the Bethe lattice",
  "title_text": "Strong-disorder expansion of the root-averaged density of states for the Anderson model on the Bethe lattice",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:25Z",
  "url": "https://research.draconitic.com/paper/eby7e91s3e5ca",
  "venue": "arXiv",
  "versions": []
}