{
  "abstract": "Let $W=n^{-1/2}\\sum_{i=1}^n X_i$, where the $X_i$ are independent centered random vectors in ${\\mathbb R}^p$ with $|X_{ij}|\\le B$ almost surely. Suppose that $\\text{Cov}(W)$ has unit diagonal and smallest eigenvalue at least $b^2>0$. We prove that the distance between $W$ and a Gaussian vector with the same covariance, uniformly over axis-aligned rectangles, is at most $C\\min\\{1,b^{-2}Bn^{-1/2}\\log^{3/2}(ep)\\}$. For fixed $b$, the dependence on summand size and dimension matches known lower bounds in growing-dimensional regimes. The proof combines a concentration estimate near rectangle boundaries with a carefully chosen Gaussian comparison.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07067",
  "author_total": 2,
  "authors": [
    {
      "name": "P. M. Aronow"
    },
    {
      "name": "Patrick Lopatto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frsxswwtwm8m1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07067",
  "fulltext_url": null,
  "id": "frsxswwtwm8m1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07067",
  "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"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7212006480",
  "pdf_url": "https://arxiv.org/pdf/2609.07067",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/frsxswwtwm8m1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07067",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07067"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal central limit theorem for bounded random variables in high dimensions",
  "title_text": "Optimal central limit theorem for bounded random variables in high dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/frsxswwtwm8m1",
  "venue": "arXiv",
  "versions": []
}