{
  "abstract": "In this note we present a dimension formula for certain randomized self-similar sets. The self-similar sets we are considering are $d$-dimensional generalizations of rational projections of inhomogeneous sponges: they have overlaps, but the overlapping structure is in some sense well-organized. The randomization happens according to a labelled Galton-Watson tree corresponding to the cylinders of the IFS, for example as in the case of the Mandelbrot percolation set. The dimension formula is given in terms of a pressure function corresponding to the expectation matrices, which describes the overlapping structure and the randomness of the system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08465",
  "author_total": 2,
  "authors": [
    {
      "name": "Vilma Orgoványi"
    },
    {
      "name": "Károly Simon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3f8f4g9r4ak45.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08465",
  "fulltext_url": null,
  "id": "3f8f4g9r4ak45",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08465",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7220936548",
  "pdf_url": "https://arxiv.org/pdf/2610.08465",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3f8f4g9r4ak45.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08465",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08465"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Dimension properties of a family of random self-similar iterated function systems",
  "title_text": "Dimension properties of a family of random self-similar iterated function systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/3f8f4g9r4ak45",
  "venue": "arXiv",
  "versions": []
}