{
  "abstract": "We study products of independent, identically distributed random matrices with an exponential moment and a simple top Lyapunov exponent, without assuming irreducibility. Outside an exceptional invariant subspace called the equator, we establish contraction on average for a weighted projective distance and a spectral gap for the associated Markov operator. We obtain a central limit theorem, a Berry--Esseen bound, deviation estimates near the mean, and an almost sure invariance principle both for the growth of a fixed vector outside the equator and for the operator norm. For fixed vectors, a non-arithmeticity assumption also yields a local limit theorem and a renewal theorem. Our contraction criterion applies more generally to mostly contracting random maps on locally compact spaces with a Lyapunov function, including certain random interval maps.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12678",
  "author_total": 2,
  "authors": [
    {
      "name": "Pablo G. Barrientos"
    },
    {
      "name": "Dominique Malicet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ccgmth96scbma.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12678",
  "fulltext_url": null,
  "id": "ccgmth96scbma",
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  "landing_url": "https://arxiv.org/abs/2610.12678",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
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      "openalex",
      "2610|Mathematical Dynamics and Fractals"
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  "openalex": "W7221559337",
  "pdf_url": "https://arxiv.org/pdf/2610.12678",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ccgmth96scbma.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12678",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12678"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Limit theorems for random matrix products with a simple top Lyapunov exponent",
  "title_text": "Limit theorems for random matrix products with a simple top Lyapunov exponent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/ccgmth96scbma",
  "venue": "arXiv",
  "versions": []
}