{
  "abstract": "We study one-dimensional marginals of an isotropic, log-concave probability measure in $\\mathbb{R}^n$. We show that the Kolmogorov distance between a typical marginal and the standard Gaussian distribution is at most $C/n$, for a universal constant $C > 0$. This bound is optimal in general, up to the value of the universal constant. It improves the Gaussian approximation bound of Bobkov, Chistyakov and Götze by a logarithmic factor in the log-concave setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16740",
  "author_total": 1,
  "authors": [
    {
      "name": "Boaz Klartag"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2b4f05h0tc52n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16740",
  "fulltext_url": null,
  "id": "2b4f05h0tc52n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16740",
  "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",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7221804342",
  "pdf_url": "https://arxiv.org/pdf/2610.16740",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2b4f05h0tc52n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16740",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16740"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Revisiting the Bobkov-Chistyakov-Götze theorem on approximately Gaussian marginals",
  "title_text": "Revisiting the Bobkov-Chistyakov-Götze theorem on approximately Gaussian marginals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/2b4f05h0tc52n",
  "venue": "arXiv",
  "versions": []
}