Multifractal analysis of measures arising from random substitutions

Random substitutions are a generalisation of (deterministic) substitutions where the substituted image of a letter is chosen from a fixed finite set with respect to a probability distribution. In contrast to their deterministic counterparts, random substitutions often give rise to positive entropy subshifts which support uncountably many ergodic measures. In this talk, I will provide an introduction to random substitutions and their associated dynamical systems, and discuss multifractal properties of a class of measures which arise naturally from random substitutions. This is joint work with Alex Rutar (University of St Andrews).