{
  "abstract": "Let $\\mu$ be a log-concave isotropic probability measure on $R^d$ , and let $\\mu^n$ denote the law of the normalized sum of $n$ independent random vectors with law $µ$. We prove that \\[ H(\\mu^n|\\gamma)\\leq \\frac{C}{n} \\min\\left\\{1+\\log(ed)^2H(\\mu|\\gamma)\\ ,\\ d\\right\\}. \\] Compared to the previous best known bound, our estimate replaces the polynomial dependence on the dimension by a polylogarithmic one. The proof relies on a new combination of the De Bruijn identity with Eldan's stochastic localization process.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31493",
  "author_total": 1,
  "authors": [
    {
      "name": "Tom Maitre"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/306gjks83v614.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31493",
  "fulltext_url": null,
  "id": "306gjks83v614",
  "issns": [],
  "landing_url": "https://hal.science/hal-05835605v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
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  "openalex": "W7223309397",
  "pdf_url": "https://hal.science/hal-05835605/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/306gjks83v614.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05835605",
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      "url": "https://hal.science/hal-05835605v1"
    },
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31493",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31493"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Improved Bounds for the Entropic Central Limit Theorem in the Log-Concave Case",
  "title_text": "Improved Bounds for the Entropic Central Limit Theorem in the Log-Concave Case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/306gjks83v614",
  "venue": "HAL",
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}