{
  "abstract": "Sudakov minoration asks whether a large family of separated random linear forms must have a large expected maximum. We present a proof candidate for this principle for all unconditional log-concave vectors. The argument starts with a classical reduction to sparse coordinate supports. It then selects one feasible threshold witness for each label, removes a common coordinate core, and controls the remaining overlaps. The main analytic step is an exponential-moment estimate for a softened witness payoff. We obtain it by combining a one-dimensional clipping inequality with triangular transport, using log-concavity of the source and sign symmetry of the target. A Bernoulli comparison restores the signs at the end. The exposition includes historical context, a guide to the proof, all intermediate arguments, and explicit choices of constants. Two consequences concern covering numbers in the moment metric and concentration of bounded functions of the magnitudes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31782",
  "author_total": 3,
  "authors": [
    {
      "name": "Witold Bednorz"
    },
    {
      "name": "Rafal Martynek"
    },
    {
      "name": "Rafal Meller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/24ge5rfjfgtvz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31782",
  "fulltext_url": null,
  "id": "24ge5rfjfgtvz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31782",
  "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.PR"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7214752027",
  "pdf_url": "https://arxiv.org/pdf/2609.31782",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/24ge5rfjfgtvz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2609.31782",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31782"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Sudakov Minoration for Unconditional Log-Concave Vectors",
  "title_text": "Sudakov Minoration for Unconditional Log-Concave Vectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/24ge5rfjfgtvz",
  "venue": "arXiv",
  "versions": []
}