  We provide a multifractal analysis of lacunary wavelet series on Cantor sets.
Byintroducing a desynchronization between the scales of the wavelets and the
scales of the steps of the construction of the Cantor set, we obtain random
processes that donot satisfy multifractal formalisms based on the Legendre
transform and on the large deviation of wavelet leaders. Subsequently, we show
how the computation of the leader large deviation spectra of "lacunarized"
versions of such wavelet series can detect the failure in the multifractal
formalism using only numerical quantities.
