{
  "abstract": "We study when the image of a measure under a random Hölder map attains full packing dimension. Our main tool is a family of packing intermediate dimension profiles $\\dim_{P,θ}^{s}μ$, indexed by $θ\\in(0,1]$ and $s>0$, which refine the packing dimension profiles of Falconer and Howroyd and reduce to them at $θ=1$. For a large family of random $α$-Hölder maps $f_ω:\\mathbb{R}^n\\to\\mathbb{R}^m$, which includes index-$α$ fractional Brownian motion as a particular case, we prove that for every compactly supported Borel probability measure $μ$ on $\\mathbb{R}^n$, $$\\dim_P μ_{f_ω}=m \\quad\\text{almost surely} \\quad\\Longleftrightarrow\\quad αm\\leq \\lim_{θ\\to 0}\\dim_{P,θ}^n μ.$$ We further study the profiles $\\dim_P^sμ$ themselves, obtaining a quantitative lower bound and a Marstrand-type identity for their limiting behavior as $θ\\to 0$. Finally, we obtain the analogous characterization for analytic sets: $$\\dim_P f_ω(E)=m \\quad\\text{almost surely} \\quad\\Longleftrightarrow\\quad αm\\leq \\lim_{θ\\to 0}\\dim_{P,θ}^n E,$$ where $\\dim_{P,θ}^n E=\\sup\\{\\dim_{P,θ}^n μ:\\, μ\\in \\mathcal{M}_c^+(E) \\}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11301",
  "author_total": 1,
  "authors": [
    {
      "name": "Nicolas Angelini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ey46h8srzy767.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11301",
  "fulltext_url": null,
  "id": "ey46h8srzy767",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11301",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7212297566",
  "pdf_url": "https://arxiv.org/pdf/2609.11301",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ey46h8srzy767.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11301",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11301"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A threshold for full packing dimension of Hölder images of sets and measures",
  "title_text": "A threshold for full packing dimension of Hölder images of sets and measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/ey46h8srzy767",
  "venue": "arXiv",
  "versions": []
}