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arXiv · 2201.00489

Measure-Theoretically Mixing Subshifts with Low Complexity

Darren Creutz·Ronnie Pavlov·Shaun Rodock
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Abstract

We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any $f : \mathbb{N} \to \mathbb{N}$ with $f(n)/n$ increasing and $\sum 1/f(n) < \infty$, that there exists an extremely elevated staircase with word complexity $p(n) = o(f(n))$. This improves the previously lowest known complexity for mixing subshifts, resolving a conjecture of Ferenczi.

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Darren Creutz, Ronnie Pavlov, Shaun Rodock. 2022-01-03. Measure-Theoretically Mixing Subshifts with Low Complexity. https://arxiv.org/abs/2201.00489

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