{
  "abstract": "Let $d\\geq 2$, $0<α<1$, and let $Γ_k$ be the successive arrival times of a standard Poisson process on $(0,\\infty)$. Given independent uniform directions $\\varepsilon_k\\in S^{d-1}$, independent of $(Γ_k)$, we consider the random countable stable zonotope $Z_α=\\bigoplus_{k=1}^{\\infty}Γ_k^{-1/α}[0,\\varepsilon_k]$. For its set of extreme points $\\operatorname{ext} Z_α$, we prove that almost surely $\\dim_H \\operatorname{ext} Z_α=(d-1)α$, and that the critical Hausdorff measure $\\mathcal H^{(d-1)α}(\\operatorname{ext} Z_α)$ is almost surely finite. The lower bound follows from the tangential non-degeneracy of the stable increments of the parametrizing field and Frostman's energy criterion. For the upper bound we construct an adaptive covering: at each scale the Poisson jumps are split into large and small ones, the large jumps determine a finite hyperplane arrangement, and the sum of the small jumps controls the diameters of the images of its cells.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28004",
  "author_total": 1,
  "authors": [
    {
      "name": "Maksim Kukushkin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/11bhzk4skh6j8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28004",
  "fulltext_url": null,
  "id": "11bhzk4skh6j8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28004",
  "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.MG"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7204834987",
  "pdf_url": "https://arxiv.org/pdf/2608.28004",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/11bhzk4skh6j8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2608.28004",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28004"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Hausdorff Dimension of the Set of Extreme Points of a Random Countable Stable Zonotope",
  "title_text": "Hausdorff Dimension of the Set of Extreme Points of a Random Countable Stable Zonotope",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/11bhzk4skh6j8",
  "venue": "arXiv",
  "versions": []
}