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Abstract. We discuss the almost sure existence of random functions that can be written as sums of elementary pulses. We then estimate their uniform Hölder regularity by applying some results on coverings by random intervals.

In this work we show that the mixed Hölder spectra of a pair of functions in a prevalent set of a product of continuous Besov spaces satisfies a mixed multifractal formalism based on the wavelet leaders. The results can be easily extended for finitely many functions in a product of continuous Besov spaces. We will use the notion of the essential shyness to calculate the mixed wavelet leaders scaling function for almost every pair of functions. As far as we know this is the first application of this notion.

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