{
  "abstract": "We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if $R_1,R_2\\in \\mathrm{SO}(d+1)$, $d\\ge 2$, generate a dense subgroup, then the random dynamics of $R_1$ and $R_2$ on $S^d$ is stably ergodic. Previously this was only known to hold in even dimensions. As a consequence, we deduce spectral gap and statistical limit theorems for such systems. In particular, our results apply in the presence of zero Lyapunov exponents.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.21199",
  "author_total": 3,
  "authors": [
    {
      "name": "Jonathan DeWitt"
    },
    {
      "name": "Dmitry Dolgopyat"
    },
    {
      "name": "Zhiyuan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7n3shpwpvsxps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.21199",
  "fulltext_url": null,
  "id": "7n3shpwpvsxps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.21199",
  "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"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7162002874",
  "pdf_url": "https://arxiv.org/pdf/2605.21199",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7n3shpwpvsxps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2605.21199",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.21199"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Ergodicity of (co)expanding on average random dynamical systems",
  "title_text": "Ergodicity of (co)expanding on average random dynamical systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/7n3shpwpvsxps",
  "venue": "arXiv",
  "versions": []
}