Journal article
Horizontally stationary generalized Bratteli diagrams
Fundamenta mathematicae, Vol.271, pp.195-225
11/21/2025
DOI: 10.4064/fm240916-6-6
Abstract
Bratteli diagrams with countably infinite levels exhibit a new phenomenon: they can be horizontally stationary. The incidence matrices of these horizontally stationary Bratteli diagrams are infinite banded Toeplitz matrices. In this paper, we study the fundamental properties of horizontally stationary Bratteli diagrams. In these diagrams, we provide an explicit description of ergodic tail invariant probability measures. For a certain class of horizontally stationary Bratteli diagrams, we prove that all ergodic tail invariant probability measures are extensions of measures from odometers. Additionally, we establish conditions for the existence of a continuous Vershik map on the path space of a horizontally stationary Bratteli diagram.
Details
- Title: Subtitle
- Horizontally stationary generalized Bratteli diagrams
- Creators
- Sergey BezuglyiPalle E.T. JorgensenOlena Karpel - Jagiellonian UniversityJan Kwiatkowski - Nicolaus Copernicus University
- Resource Type
- Journal article
- Publication Details
- Fundamenta mathematicae, Vol.271, pp.195-225
- DOI
- 10.4064/fm240916-6-6
- ISSN
- 0016-2736
- eISSN
- 1730-6329
- Publisher
- POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN
- Grant note
- NCN (National Science Centre, Poland): 2019/35/D/ST1/01375 Polish Ministry of Science and Higher Education
O.K. is supported by the NCN (National Science Centre, Poland) Grant 2019/35/D/ST1/01375 and by the program "Excellence Initiative-Research University" for the AGH University of Krakow. O.K. also acknowledges partial support by a subsidy from the Polish Ministry of Science and Higher Education.
- Language
- English
- Date published
- 11/21/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9985034933302771
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