{
  "abstract": "We prove the Sudakov minoration principle, with a universal constant, for unconditional log-concave random vectors whose coordinate magnitudes are negatively associated. The main step is a deterministic selection theorem: pairwise witnesses in convex downwardclosed sets yield, on an exponentially large subfamily, one fixed witness per label separating it from every other retained label. The selection combines a prefix counting inequality with convex separation in the space of all label-coordinate arrays. Negative association then controls the expected number of active joint-tail witnesses, while a Bernoulli argument on complementary coordinate sets retains the random signs. The proof uses joint upper-orthant probabilities and applies negative association only under the original law. Consequences include minoration for products of Orlicz-based log-concave measures and a covering estimate in the moment metric, expressed geometrically through polar Lp centroid bodies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30525",
  "author_total": 3,
  "authors": [
    {
      "name": "Witold Bednorz"
    },
    {
      "name": "Rafal Martynek"
    },
    {
      "name": "Rafal Meller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c269g24pab3n8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30525",
  "fulltext_url": null,
  "id": "c269g24pab3n8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30525",
  "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": "W7214626527",
  "pdf_url": "https://arxiv.org/pdf/2609.30525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c269g24pab3n8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Sudakov minoration for unconditional log-concave vectors with negatively associated magnitudes",
  "title_text": "Sudakov minoration for unconditional log-concave vectors with negatively associated magnitudes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/c269g24pab3n8",
  "venue": "arXiv",
  "versions": []
}