{
  "abstract": "We prove a finite-entropy criterion for the entropic conditional central limit theorem. Let $(ξ_i,η_i)_{i\\geq 1}$ be independent copies of a pair $(ξ,η)$, and set $W_n=n^{-1/2}\\sum_{i=1}^n ξ_i$ and $\\boldsymbolη_n=(η_1,\\ldots,η_n)$. Under the assumptions that $\\mathbb{E}\\operatorname{Var}(ξ\\midη)<\\infty$ and that the conditional law of $ξ$ given $η$ is absolutely continuous almost surely, we show that $\\mathbb{E}h(W_n\\mid\\boldsymbolη_n)$ converges to the Gaussian entropy $\\frac12\\log(2πeσ^2)$, where $σ^2=\\mathbb{E}\\operatorname{Var}(ξ\\midη)$, if and only if $\\mathbb{E}h(W_{n_0}\\mid\\boldsymbolη_{n_0})>-\\infty$ for some $n_0$. The main technical ingredient is a continuity theorem for Fisher information under Gaussian smoothing, which allows us to replace the finite expected conditional Fisher-information assumption by a necessary and sufficient finite-entropy condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30579",
  "author_total": 4,
  "authors": [
    {
      "name": "Tong Ye"
    },
    {
      "name": "Liu-Quan Yao"
    },
    {
      "name": "Shuai Yuan"
    },
    {
      "name": "Guanghui Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9c4pdjgd9z4ch.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30579",
  "fulltext_url": null,
  "id": "9c4pdjgd9z4ch",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30579",
  "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",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7204922225",
  "pdf_url": "https://arxiv.org/pdf/2608.30579",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9c4pdjgd9z4ch.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30579",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30579"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Finite-Entropy Criterion for the Entropic Conditional Central Limit Theorem",
  "title_text": "A Finite-Entropy Criterion for the Entropic Conditional Central Limit Theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/9c4pdjgd9z4ch",
  "venue": "arXiv",
  "versions": []
}