{
  "abstract": "For $0<κ<8$, we prove a uniform dimension transformation theorem for SLE in natural time: on a single probability-one event, Hausdorff and packing dimensions of every time set are multiplied by $d=1+κ/8$, and the same holds for lower and upper box dimensions of every bounded time set. The result applies to self-similar SLE with stationary increments, chordal SLE in the half-plane, and chordal SLE in bounded piecewise $C^1$ Jordan domains. In the last case, the box-dimension conclusion holds under a positive-angle endpoint hypothesis. We also establish boundary-inclusive local Hölder continuity of every order below $1/d$ for chordal SLE in natural time and identify the exact local dimension $d$ of the natural occupation measure on compact time intervals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02493",
  "author_total": 1,
  "authors": [
    {
      "name": "Dapeng Zhan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7w9frv278qny.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02493",
  "fulltext_url": null,
  "id": "d7w9frv278qny",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02493",
  "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/2611.02493",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7w9frv278qny.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02493",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02493"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Uniform Dimension Theorem for SLE in Natural Time",
  "title_text": "Uniform Dimension Theorem for SLE in Natural Time",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/d7w9frv278qny",
  "venue": "arXiv",
  "versions": []
}