{
  "abstract": "Let $Y_1,\\ldots,Y_n$ be independent symmetric random variables with log-concave tails. We give a dimension-free characterization of the expected supremum of the canonical process $X_x=\\sum_{i=1}^n x_iY_i$ without any $Δ_2$ or regular-growth assumption on the coordinate tails. The characterization is governed by scale-dependent intrinsic costs determined directly by the convex tail potentials. It has an information-theoretic rate-distortion formulation as well as two equivalent majorizing-measure formulations on the original index set, one multiscale and one based on a single probability measure. More strongly, the comparison holds for every prescribed law of the index. In particular, the Gaussian majorizing-measure theorem of Talagrand and the Bernoulli theorem of Bednorz-Latała are recovered from the same formula, through quadratic and truncated quadratic costs, respectively. The new geometry is necessary: once the $Δ_2$ growth condition is removed, the usual chaining functional based on increment moments can exceed the expected supremum by an unbounded factor. The proof is based on a uniform convex-order truncation principle for symmetric exponentials and a dyadic decomposition of the tail slopes that transfers simultaneously the random process and its intrinsic cost, with universal constants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13959",
  "author_total": 3,
  "authors": [
    {
      "name": "Xuanang Hu"
    },
    {
      "name": "Hanchao Wang"
    },
    {
      "name": "Xinglong Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/45et5n2cj9dtf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13959",
  "fulltext_url": null,
  "id": "45et5n2cj9dtf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13959",
  "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.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7213230892",
  "pdf_url": "https://arxiv.org/pdf/2609.13959",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/45et5n2cj9dtf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13959",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13959"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Majorizing Measures for Canonical Processes with Log-Concave Tails",
  "title_text": "Majorizing Measures for Canonical Processes with Log-Concave Tails",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/45et5n2cj9dtf",
  "venue": "arXiv",
  "versions": []
}