Topological Mixing of Random Substitutions

• المؤلفون الرئيسيون: Miro, Eden Delight, Rust, Dan, Sadun, Lorenzo, Tadeo, Gwendolyn
• التنسيق: text
• منشور في: Archīum Ateneo 2022
• الموضوعات: Mathematics; Physical Sciences and Mathematics
• الوصول للمادة أونلاين: https://archium.ateneo.edu/mathematics-faculty-pubs/227; https://doi.org/10.1007/s11856-022-2406-3
• المؤسسة: Ateneo De Manila University

We investigate topological mixing of compatible random substitutions. For primitive random substitutions on two letters whose second eigenvalue is greater than one in modulus, we identify a simple, computable criterion which is equivalent to topological mixing of the associated subshift. This generalises previous results on deterministic substitutions. In the case of recognisable, irreducible Pisot random substitutions, we show that the associated subshift is not topologically mixing. Without recognisability, we rely on more specialised methods for excluding mixing and we apply these methods to show that the random Fibonacci substitution subshift is not topologically mixing.