Bratteli diagrams where random orders are imperfect
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- by J. Janssen, A. Quas and R. Yassawi PDF
- Proc. Amer. Math. Soc. 145 (2017), 721-735 Request permission
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 $B$, a random order on $B$ does not admit a continuous Vershik map.References
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Additional Information
- J. Janssen
- Affiliation: Department of Mathematics and Statistics, Dalhousie University, 6316 Coburg Road, P.O. Box 15000, Halifax, Nova Scotia, Canada
- MR Author ID: 289540
- Email: Jeannette.Janssen@dal.ca
- A. Quas
- Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada
- MR Author ID: 317685
- Email: aquas@uvic.ca
- R. Yassawi
- Affiliation: Department of Mathematics, Trent University, 1600 West Bank Drive, Peterborough, ON, Canada
- MR Author ID: 662381
- Email: ryassawi@trentu.ca
- Received by editor(s): June 22, 2015
- Received by editor(s) in revised form: April 13, 2016
- Published electronically: October 31, 2016
- Additional Notes: The first two authors were partially supported by NSERC Discovery Grants
- Communicated by: Nimish Shah
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 721-735
- MSC (2010): Primary 37B10; Secondary 37A20
- DOI: https://doi.org/10.1090/proc/13284
- MathSciNet review: 3577873