The Graph and Range Singularity Spectra of Random Wavelet Series built from Gibbs measures

Abstract

We consider multifractal random wavelet series built from Gibbs measures, and study the singularity spectra associated with the graph and range of these functions restricted to their iso-H\"older sets. To obtain these singularity spectra, we use a family of Gibbs measures defined on a sequence of topologically transitive subshift of finite type whose Hausdorff distance to the set of zeros of the mother wavelet tends to 0.