Dan Rust

Dynamics of random substitution

Substitutions are rules for mapping letters in an alphabet to words over that alphabet, with the goal of iterating such a map to generate interesting infinite words. A random substitution is a generalisation of a substitution, where one has a finite set of possible image words that are independently chosen each time the random substitution is applied to each of the letters in a word. This gives rise to infinite words that share similar long-range order properties with substitutive words, but which differ in their local order because they exhibit positive entropy. I will give an overview of this class of systems from a dynamical perspective and some of the aspects that have recently been studied.