Multifractal formalism for inverse measures of random weak Gibbs measures
arXiv:1701.05734
Abstract
Any Borel probability measure supported on a Cantor set of zero Lebesgue measure on the real line possesses a discrete inverse measure. We study the validity of the multifractal formalism for the inverse measures of random weak Gibbs measures supported on the attractor associated with some random dynamics encoded by a random subshift of finite type, and expanding in the mean. The study requires, in particular, to develop in this context of random dynamics a suitable extension of the results known for heterogeneous ubiquity associated with deterministic Gibbs measures.