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arXiv · 1309.1855

Bounded rank-one transformations

Su Gao·Aaron Hill
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Abstract

We define the notion of canonical boundedness among rank-one transformations and use it to characterize the class of all bounded rank-one transformations with trivial centralizer. We also explicitly characterize totally ergodic rank-one transformations with bounded cutting parameter. Together with a recent result of Ryzhikov our results provide a simple procedure for determining whether a bounded rank-one transformation has minimal self-joinings of all orders purely in terms of the cutting and spacer parameters for the transformation.

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Su Gao, Aaron Hill. 2013-09-07. Bounded rank-one transformations. https://arxiv.org/abs/1309.1855

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