We prove that the Hölder singularities of random lacunary wavelet series are chirps located on random fractal sets. We determine the Hausdorff dimensions of these singularities, and the a.e. modulus of continuity of the series. Lacunary wavelet series thus turn out to be a new example of multifractal functions.
"On lacunary wavelet series." Ann. Appl. Probab. 10 (1) 313 - 329, February 2000. https://doi.org/10.1214/aoap/1019737675