Mixing properties and entropy bounds of a family of Pisot random substitutions

• Main Authors: Escolano, Giovanni B, Mañibo, Neil, Miro, Eden Delight
• Format: text
• Published: Archīum Ateneo 2022
• Subjects: Pisot numbers; Random substitution subshifts; Recognisable words; Topological entropy; Topological mixing; Geometry and Topology; Mathematics; Physical Sciences and Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/219; https://doi.org/10.1016/j.indag.2022.04.004
• Institution: Ateneo De Manila University

We consider a two-parameter family of random substitutions and show certain combinatorial and topological properties they satisfy. We establish that they admit recognisable words at every level. As a consequence, we get that the subshifts they define are not topologically mixing. We then show that they satisfy a weaker mixing property using a numeration system arising from a sequence of lengths of inflated words. Moreover, we provide explicit bounds for the corresponding topological entropy in terms of the defining parameters n and p.