Abstract
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.
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Acknowledgements
It is a pleasure to thank M. Baake, D. Frettlöh, F. Gähler and N. Mañibo for helpful discussions. EDM would like to acknowledge the support of the Alexander von Humboldt Foundation and Ateneo de Manila University. DR was supported by the German Research Foundation (DFG), within the CRC 1283 at Bielefeld University, where the majority of the research was conducted. GT would like to thank the Commission on Higher Education (CHED) of the Philippines for support.
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Miro, E.D., Rust, D., Sadun, L. et al. Topological mixing of random substitutions. Isr. J. Math. 255, 123–153 (2023). https://doi.org/10.1007/s11856-022-2406-3
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DOI: https://doi.org/10.1007/s11856-022-2406-3