Multifractal formalism for the inverse of random weak Gibbs measures

Abstract

Any Borel probability measure supported on a Cantor set included in [Formula: see text] and 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. The study requires, in particular, to develop in this context of random dynamics a suitable version of the results known for heterogeneous ubiquity associated with deterministic Gibbs measures.