Janssen, JeannetteQuas, AnthonyYassawi, Reem2019-04-052019-04-0520172017Janssen, 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/13284http://dx.doi.org/10.1090/proc/13284http://hdl.handle.net/1828/10692For 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.enBratteli diagramsVershik mapsPostprint