{
  "abstract": "We prove that the martingale dimension of a broad class of strongly local regular Dirichlet forms is bounded above by a small-scale version of spectral dimension. This resolves a conjecture of Hino for this class of spaces, extending his earlier results beyond self-similar fractals. Our proof uses differentiation of energy measures to select good blow-up scales and construct approximately harmonic coordinates. We then study weak limits of their Euclidean image measures and combine an integration-by-parts argument with uniform Sobolev inequalities to establish the dimension bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39312",
  "author_total": 2,
  "authors": [
    {
      "name": "Aobo Chen"
    },
    {
      "name": "Mathav Murugan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnxpncd0d3q46.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39312",
  "fulltext_url": null,
  "id": "bnxpncd0d3q46",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39312",
  "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.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39312",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnxpncd0d3q46.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39312",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39312"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Bounding martingale dimension by spectral dimension",
  "title_text": "Bounding martingale dimension by spectral dimension",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/bnxpncd0d3q46",
  "venue": "arXiv",
  "versions": []
}