{
  "abstract": "A surprisingly wide variety of important random fractal metric spaces in modern probability theory can be viewed as self-similar random quotients of the real line, including the continuum random tree, Liouville quantum gravity surfaces, the trace of Brownian motion in $\\mathbb{R}^d$, and self-similar ($s=2d$) long-range percolation on $\\mathbb{R}$. We prove that the metric and resistance growth dimensions are well-defined in a certain sense for every random metric space in a class containing all of the above examples. Our results are new for the trace of Brownian motion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39953",
  "author_total": 2,
  "authors": [
    {
      "name": "Johannes Bäumler"
    },
    {
      "name": "Tom Hutchcroft"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6gnsd311q0g9q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39953",
  "fulltext_url": null,
  "id": "6gnsd311q0g9q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39953",
  "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/2610.39953",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6gnsd311q0g9q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39953",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39953"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On self-similar random quotients of the line",
  "title_text": "On self-similar random quotients of the line",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/6gnsd311q0g9q",
  "venue": "arXiv",
  "versions": []
}