Bratteli diagrams where random orders are imperfect
Dynamical Systems
2016-06-13 v3
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 level-n 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, a random order on B does not admit a continuous Vershik map.
Cite
@article{arxiv.1407.3496,
title = {Bratteli diagrams where random orders are imperfect},
author = {Jeannette Janssen and Anthony Quas and Reem Yassawi},
journal= {arXiv preprint arXiv:1407.3496},
year = {2016}
}
Comments
14 pages, 1 figure. The exposition incorporates the referee's remarks. arXiv admin note: text overlap with arXiv:1503.03360 by other authors