{
  "abstract": "Through the seminal works of Peligrad and Bradley, the existing sufficient conditions for the central limit theorem for $ρ$-mixing sequences are known to be very close to necessary. Nevertheless, we show that further improvements to these conditions are achievable when the $ρ$-mixing coefficients are non-summable, bridging a long-standing gap in the borderline case. The key idea is an iterative block-size technique that enables precise evaluations of the slowly varying variance components. Finally, known examples and new extensions--including iterated logarithmic mixing rates--are investigated to demonstrate the sharpness of our criteria, revealing a clear parameter structure and posing related open problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04638",
  "author_total": 1,
  "authors": [
    {
      "name": "Muneya Matsui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dv65tp2475ad2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04638",
  "fulltext_url": null,
  "id": "dv65tp2475ad2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04638",
  "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"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7211894970",
  "pdf_url": "https://arxiv.org/pdf/2609.04638",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dv65tp2475ad2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04638",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04638"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Can we further improve the central limit theorem for stationary $ρ$-mixing sequences $?$",
  "title_text": "Can we further improve the central limit theorem for stationary ρ-mixing sequences ?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:25Z",
  "url": "https://research.draconitic.com/paper/dv65tp2475ad2",
  "venue": "arXiv",
  "versions": []
}