{
  "abstract": "Let $P$ be a Markov operator on a general state space $(S,\\Sigma)$ with invariant probability $m$, assumed ergodic. When $P$ is normal in $L_2(m)$, we prove the necessity of uniform ergodicity, under some spectral conditions (satisfied when $P$ is symmetric), for the annealed CLT to hold for {\\it every} centered $ f \\in L_2(m)$. We also obtain results without assuming normality under some Ritt-type conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02282",
  "author_total": 2,
  "authors": [
    {
      "name": "Christophe Cuny"
    },
    {
      "name": "Michael Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2pbgqewq30873.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02282",
  "fulltext_url": null,
  "id": "2pbgqewq30873",
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  "landing_url": "https://hal.science/hal-05769894v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
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      "1.math.math-pr"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05769894/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2pbgqewq30873.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05769894",
      "source": "hal",
      "url": "https://hal.science/hal-05769894v1"
    },
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02282",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02282"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Global Central Limit Theorems for Markov chains with normal transition operator",
  "title_text": "Global Central Limit Theorems for Markov chains with normal transition operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/2pbgqewq30873",
  "venue": "HAL",
  "versions": []
}