Mixing properties and entropy bounds of a family of Pisot random substitutions
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.
Escolano, G.B., Mañibo, N., & Miro, E.D. (2022). Mixing properties and entropy bounds of a family of Pisot random substitutions. Indagationes Mathematicae, 33(5), 965-991. https://doi.org/10.1016/j.indag.2022.04.004