{
  "abstract": "Let $(M,τ)$ be a semifinite von Neumann algebra, let $J$ be a trace-preserving Jordan isomorphism, and let $(n_k)_{k\\geq 1}$ be a random increasing sequence of integers obtained by selecting each integer $n\\geq 1$ independently with probability $n^{-α}$, where $0<α<\\frac12$. We show that, almost surely, for every $x\\in L^1(M)$, $ \\frac1m\\sum_{k=1}^m J^{n_k}(x)$ converges bilaterally almost uniformly. This extends LaVictoire's classical random $L^1$ ergodic theorem to the non-commutative setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07970",
  "author_total": 3,
  "authors": [
    {
      "name": "Léonard Cadilhac"
    },
    {
      "name": "Christian Le Merdy"
    },
    {
      "name": "Safoura Zadeh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/694eymbgz2ae6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07970",
  "fulltext_url": null,
  "id": "694eymbgz2ae6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07970",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7212045734",
  "pdf_url": "https://arxiv.org/pdf/2609.07970",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/694eymbgz2ae6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07970",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07970"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Non-commutative Individual Ergodic Theorem Along Sparse Random Subsequences",
  "title_text": "A Non-commutative Individual Ergodic Theorem Along Sparse Random Subsequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/694eymbgz2ae6",
  "venue": "arXiv",
  "versions": []
}