{
  "abstract": "Characterizations are established regarding the existence of an $L^2$-spectral gap for ergodic (that is, irreducible, aperiodic, and positive) Markov chains on infinite state spaces. In particular, it is shown that the existence of an $L^2$-spectral gap is entirely determined by the behavior of the spectrum at 1. These results are applied in the analysis of a family of Markov chains constructed to show that the ergodic composition of two geometrically ergodic Markov kernels need not be geometrically ergodic.",
  "abstract_shown": true,
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  "article_type": null,
  "arxiv": "2610.24808",
  "author_total": 2,
  "authors": [
    {
      "name": "Xavier Mak"
    },
    {
      "name": "James P. Hobert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0wrervy24z4w7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24808",
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      "2613|Markov Chains and Monte Carlo Methods"
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  "pdf_url": "https://arxiv.org/pdf/2610.24808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0wrervy24z4w7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24808"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
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    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
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  ],
  "title": "On the existence of a spectral gap for ergodic Markov chains",
  "title_text": "On the existence of a spectral gap for ergodic Markov chains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/0wrervy24z4w7",
  "venue": "arXiv",
  "versions": []
}