Generalized Bratteli diagrams without probability tail invariant measures

Andrew Barsky; Sergey Bezuglyi

doi:10.48550/arxiv.2609.14275

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Generalized Bratteli diagrams without probability tail invariant measures

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Generalized Bratteli diagrams without probability tail invariant measures

Andrew Barsky and Sergey Bezuglyi

arXiv

09/13/2026

DOI: 10.48550/arxiv.2609.14275

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https://doi.org/10.48550/arxiv.2609.14275View

Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

The paper focuses on the following problem: given a generalized Bratteli diagramB , determine conditions under which the tail equivalence relation𝓡does not admit a tail invariant probability measure on the path spaceX_(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.

Mathematics - Dynamical Systems

Mathematics - Probability

Details

Title: Subtitle: Generalized Bratteli diagrams without probability tail invariant measures
Creators: Andrew Barsky
Sergey Bezuglyi
Resource Type: Preprint
Publication Details: arXiv
DOI: 10.48550/arxiv.2609.14275
ISSN: 2331-8422
Publisher: arXiv
Language: English
Date posted: 09/13/2026
Academic Unit: Mathematics
Record Identifier: 9985230926502771

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