{
  "abstract": "Can the Alexander-Orbach conjecture hold on hierarchical lattices? We construct Gromov-Hausdorff-Prokhorov scaling limits of critical percolation clusters on hierarchical lattices in the chemical metric and determine the typical spectral dimensions of the associated diffusions. These dimensions are dense in $(1,2)$; however, outside a narrow region in dimension space, we prove that the Alexander-Orbach conjecture fails on every hierarchical lattice under consideration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16875",
  "author_total": 1,
  "authors": [
    {
      "name": "Ziyu Neroli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/88y0be3mk7pag.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16875",
  "fulltext_url": null,
  "id": "88y0be3mk7pag",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16875",
  "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",
      "cond-mat.stat-mech"
    ],
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.MP"
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      "math.PR"
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      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7221768100",
  "pdf_url": "https://arxiv.org/pdf/2610.16875",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/88y0be3mk7pag.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.16875",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16875"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Iterated Graph Systems (III): Alexander-Orbach conjecture on hierarchical lattices",
  "title_text": "Iterated Graph Systems (III): Alexander-Orbach conjecture on hierarchical lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/88y0be3mk7pag",
  "venue": "arXiv",
  "versions": []
}