Bratelli Diagrams Where Random Orders are Imperfect
Date
2017
Authors
Janssen, Jeannette
Quas, Anthony
Yassawi, Reem
Journal Title
Journal ISSN
Volume Title
Publisher
Proceedings of the American Mathematical Society
Abstract
For the simple Bratteli diagrams B where there is a single edge connecting any two vertices in consecutive levels, we show that a random order has uncountably many infinite paths if and only if the growth rate of the leveln vertex sets is super-linear. This gives us the dichotomy: a random order on a slowly growing Bratteli diagram admits a homeomorphism, while a random order on a quickly growing Bratteli diagram does not. We also show that for a large family of infinite rank Bratteli diagrams B, a random order on B does not admit a continuous Vershik map.
Description
Keywords
Bratteli diagrams, Vershik maps
Citation
Janssen, J.; Quas, A.; & Yassawi, R. (2017). Bratelli diagrams where random orders are imperfect. Proceedings of the American Mathematical Society, 145(2), 721-735. http://dx.doi.org/10.1090/proc/13284