{
  "abstract": "Let $M$ be a closed Riemannian surface, and let $f_1,\\ldots,f_s$ be area-preserving $C^2$ diffeomorphisms with fixed positive probabilities such that the resulting random dynamical system is uniformly expanding on average. For each $n$, choose $ω_1,\\ldots,ω_n$ independently according to these probabilities and set $F=f_{ω_n}\\circ\\cdots\\circ f_{ω_1}$. We prove that there exists $α>0$ such that, with probability at least $1-e^{-αn}$, the correlations of any two Hölder observables $ϕ,ψ$ under $F^m$ are bounded by $e^{-αn}\\|ϕ\\|_{C^β}\\|ψ\\|_{C^β}$, for all $m\\leq e^{αn}$. These estimates imply a law of large numbers and a central limit theorem for the Birkhoff sums along $F$ of any zero-mean Hölder observable $ϕ$, for exponentially long times in $n$. The limiting Gaussian has variance $\\int_Mϕ^2\\,d\\mathrm{vol}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42083",
  "author_total": 3,
  "authors": [
    {
      "name": "Dmitry Dolgopyat"
    },
    {
      "name": "Bassam Fayad"
    },
    {
      "name": "Alexey Okunev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77y1htxp5qza5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42083",
  "fulltext_url": null,
  "id": "77y1htxp5qza5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42083",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.42083",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77y1htxp5qza5.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42083",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42083"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Long-time stochasticity for periodic iterations of random surface maps",
  "title_text": "Long-time stochasticity for periodic iterations of random surface maps",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/77y1htxp5qza5",
  "venue": "arXiv",
  "versions": []
}