{
  "abstract": "The paper focuses on the following problem: given a generalized Bratteli diagram $B$, determine conditions under which the tail equivalence relation $\\mathcal R$ does not admit a tail invariant probability measure on the path space $X_B$. We give several sufficient conditions, formulated in terms of the incidence matrices, that guarantee the nonexistence of such a measure. We also discuss a new spectral method for finding tail invariant measures for a class of stationary generalized Bratteli diagrams. This method allowed us to answer affirmatively an open problem formulated in arXiv:2212.13803.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14275",
  "author_total": 2,
  "authors": [
    {
      "name": "Andrew Barsky"
    },
    {
      "name": "Sergey Bezuglyi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6f50bph8yvmwf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14275",
  "fulltext_url": null,
  "id": "6f50bph8yvmwf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14275",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7213320572",
  "pdf_url": "https://arxiv.org/pdf/2609.14275",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6f50bph8yvmwf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.14275",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14275"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Generalized Bratteli diagrams without probability tail invariant measures",
  "title_text": "Generalized Bratteli diagrams without probability tail invariant measures",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/6f50bph8yvmwf",
  "venue": "arXiv",
  "versions": []
}