{
  "abstract": "Let $2\\le m < n$ be integers, and let $K(\\mathcal{A})$ be the Bedford--McMullen carpet generated by $\\{(x,y)\\mapsto((x+i)/m,(y+j)/n):(i,j)\\in\\mathcal{A}\\}$, where $\\mathcal{A}$ is a subset of $\\{0,1,\\ldots,m-1\\}\\times\\{0,1,\\ldots,n-1\\}$. Write $\\mathcal{B}$ for the set of occupied columns, and assume that $\\#\\mathcal{B}\\ge2$ and each column contains at least two symbols of $\\mathcal{A}$. At each vertex of the column tree $\\mathcal{B}^*$, we independently choose one forbidden symbol from $\\mathcal{A}$ according to a prescribed distribution. Let $\\mathbb{P}$ denote the resulting product measure on $\\mathcal{A}^{\\mathcal{B}^*}$. This gives a random survivor set $K_ω(\\mathcal{A})$ with $ω\\in\\mathcal{A}^{\\mathcal{B}^*}$. We show that, for $\\mathbb{P}$-a.e. $ω$, \\begin{equation*} \\dim_H K_ω(\\mathcal{A})=\\frac{1}{\\log m}\\log\\left(\\int \\sum_{b\\in\\mathcal{B}}\\ell_b(ω)^{\\frac{\\log m}{\\log n}} d\\mathbb{P}(ω)\\right), \\end{equation*} where $\\ell_b(ω)$ is the number of surviving symbols in column $b$ at the root.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31440",
  "author_total": 3,
  "authors": [
    {
      "name": "Derong Kong"
    },
    {
      "name": "Cai-Yun Ma"
    },
    {
      "name": "Károly Simon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/617nz1da028ap.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31440",
  "fulltext_url": null,
  "id": "617nz1da028ap",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31440",
  "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.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7223300991",
  "pdf_url": "https://arxiv.org/pdf/2610.31440",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/617nz1da028ap.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31440",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31440"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Random Survivor Sets with Moving Holes in Bedford-McMullen Carpets",
  "title_text": "Random Survivor Sets with Moving Holes in Bedford-McMullen Carpets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/617nz1da028ap",
  "venue": "arXiv",
  "versions": []
}