PreprintCC BY 4.0arXiv
Generalized Bratteli diagrams without probability tail invariant measures
Abstract
The paper focuses on the following problem: given a generalized Bratteli diagram B, determine conditions under which the tail equivalence relation ℛ does not admit a tail invariant probability measure on the path space XB. 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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BibTeX
@misc{barsky2026generalized,
title = {{Generalized Bratteli diagrams without probability tail invariant measures}},
author = {Andrew Barsky and Sergey Bezuglyi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.14275},
eprint = {2609.14275},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14275},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generalized Bratteli diagrams without probability tail invariant measures
AU - Andrew Barsky
AU - Sergey Bezuglyi
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2609.14275
UR - https://arxiv.org/abs/2609.14275
AB - The paper focuses on the following problem: given a generalized Bratteli diagram B, determine conditions under which the tail equivalence relation 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.
ER -