Measure-Theoretically Mixing Subshifts with Low Complexity

2022/01/03 by Darren Creutz, Creutz, Darren, Ronnie Pavlov +3
Computer Science · #Algorithms and Data Compression #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Primary: 37B10 #Secondary: 37A25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2201.00489

openalex publication_date 2022/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 : ℕ → ℕ with f(n)/n increasing and ∑ 1/f(n) < ∞, 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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