The graph and range singularity spectra of random wavelet series built from Gibbs measures

We consider the random wavelet series built from Gibbs measures, and study the Hausdorff dimension of the graph and range of these functions restricted to their iso-Hölder sets. To obtain the Hausdorff dimension of these sets, we apply the potential theoretic method to families 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.