{
  "abstract": "We introduce a one-parameter family of notions between double ergodicity and metric ergodicity for measure-class preserving (i.e., nonsingular) actions of countable groups on standard probability spaces, providing infinitely many new invariants distinguishing weakly mixing actions. We call these properties (essentially) $k$-chaining, for $k \\in \\mathbb{N}$. We apply this framework to study boundary actions of free groups of finite rank $r \\ge 1$, where the boundary is equipped with a stationary Markov measure. We prove that in this context, weak mixing is equivalent to $(2r-1)$-chaining, as well as to strict irreducibility of the transition matrix of the Markov measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18061",
  "author_total": 2,
  "authors": [
    {
      "name": "Anush Tserunyan"
    },
    {
      "name": "Jenna Zomback"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2dhw17n76b3tk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18061",
  "fulltext_url": null,
  "id": "2dhw17n76b3tk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18061",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7213500815",
  "pdf_url": "https://arxiv.org/pdf/2609.18061",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2dhw17n76b3tk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.18061",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18061"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Bounded chaining in measurable dynamics",
  "title_text": "Bounded chaining in measurable dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/2dhw17n76b3tk",
  "venue": "arXiv",
  "versions": []
}