Bratteli diagrams where random orders are imperfect release_3b2qea6y3vcffjwowo6poh4jyi

by Jeannette Janssen, Anthony Quas, Reem Yassawi

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2016  

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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Type  article
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Date   2016-06-10
Version   v3
Language   en ?
arXiv  1407.3496v3
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