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arXiv · 2609.14275

Generalized Bratteli diagrams without probability tail invariant measures

Andrew Barsky·Sergey Bezuglyi
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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.

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BibTeXRIS

Andrew Barsky, Sergey Bezuglyi. 2026-09-13. Generalized Bratteli diagrams without probability tail invariant measures. https://arxiv.org/abs/2609.14275

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