{
  "abstract": "In his highly influential paper, \\emph{On the maximal ergodic theorem for certain subsets of the integers}, Bourgain introduced the study of pointwise convergence of ergodic averages along randomly generated subsets of the integers, developing a robust \\(L^p\\)-theory for \\(p>1\\). More recently, this theory was partially complemented at the \\(L^1\\) endpoint by work of LaVictoire, who treated averages along random sequences that are ``slightly denser\" than the set of squares, for which universal \\(L^1\\) pointwise convergence is known to fail. In this work, we prove that, almost surely, for every measure-preserving system and every integrable function, the ergodic averages formed by sampling along random sequences with quadratic growth converge almost everywhere. Our proof combines harmonic-analytic methods developed by M.~Christ with a ``random sampling\" of quadratic forms, thereby overcoming the main uniformity obstruction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04106",
  "author_total": 3,
  "authors": [
    {
      "name": "Will Burstein"
    },
    {
      "name": "Lorenzo Catani"
    },
    {
      "name": "Ben Krause"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4yq7w09gmag0g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04106",
  "fulltext_url": null,
  "id": "4yq7w09gmag0g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04106",
  "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.CA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.04106",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4yq7w09gmag0g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04106",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04106"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Pointwise Convergence of Random Ergodic Averages at the \\(L^1\\) Endpoint",
  "title_text": "Pointwise Convergence of Random Ergodic Averages at the L^1 Endpoint",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4yq7w09gmag0g",
  "venue": "arXiv",
  "versions": []
}