{
  "abstract": "An Orlicz ball is the set of points where the sum of a fixed even convex function of the coordinates does not exceed a given radius, here proportional to the dimension. For a broad class of such functions, including non-homogeneous ones, we find the exponential rate of the intrinsic volumes whose order is proportional to the dimension and express it by a two-parameter variational formula involving only one-dimensional integrals. As a function of the order-to-dimension ratio, this rate is concave and continuous on the closed unit interval, and the convergence is uniform in the order. This proves the exponential-profile conjecture of Kabluchko, Marynych, and Prochno for these bodies and recovers their result for $\\ell_p$ balls with $p>1$. The proof relies on the theory of large deviations. An exact formula for the Laplace transform of the intrinsic volumes in the radius, extending theirs for $\\ell_p$ balls, plays the role of a moment generating function, and a Laplace method gives its exponential rate. An exponential change of measure, analogous to that used in Cramér's theorem, then recovers the intrinsic volumes. The key step is a lower bound on the tilted density at its mean, obtained from log-concavity rather than a law of large numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16904",
  "author_total": 1,
  "authors": [
    {
      "name": "Mykyta Sadok"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74e1bnr6x0ft3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16904",
  "fulltext_url": null,
  "id": "74e1bnr6x0ft3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16904",
  "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": "W7221786763",
  "pdf_url": "https://arxiv.org/pdf/2610.16904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74e1bnr6x0ft3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:16Z",
      "native_id": "2610.16904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Exponential profiles for the intrinsic volumes of Orlicz balls",
  "title_text": "Exponential profiles for the intrinsic volumes of Orlicz balls",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/74e1bnr6x0ft3",
  "venue": "arXiv",
  "versions": []
}