Bratteli diagrams where random orders are imperfect

Jeannette Janssen; Anthony Quas; Reem Yassawi

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arXiv · 1407.3496

Bratteli diagrams where random orders are imperfect

Jeannette Janssen·Anthony Quas·Reem Yassawi

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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.

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Jeannette Janssen, Anthony Quas, Reem Yassawi. 2014-07-13. Bratteli diagrams where random orders are imperfect. https://arxiv.org/abs/1407.3496

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