Measure Theoretic Entropy of Random Substitution Subshifts

Abstract Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory quasicrystals). Two their most striking features that they have low complexity (zero topological entropy) uniquely ergodic. Random a generalisation where the substituted image letter is determined by Markov process. In stark contrast to counterparts, subshifts random often positive entropy, support uncountably many ergodic measures. The underlying process singles out one measures, called frequency measure. Here, we develop new techniques for computing studying entropy these As an application our results, obtain closed form formulas measures wide range substitution show cases there exists measure maximal entropy. Further, class subshifts, prove this unique These do not satisfy Bowen’s specification property or weaker Climenhaga Thompson hence provide interesting intrinsically subshifts.