Régularité des séries aléatoires d'ondelettes en termes de p-exposants

We study the regularity of Random Wavelet Series through the determination of their p-spectrum of singularities, i.e. the Hausdorff dimension of the sets of points sharing a given p-exponent. Random Wavelet Series have been introduced by J.-M. Aubry and S. Jaffard in 2002 and are obtained by drawing randomly and independently wavelet coefficients at each scale according to a given sequence of probability laws. The aim is to extend the results known since then about their Hölder spectrum of singularities (corresponding to the case p=+\infty) by letting p takes any value in (0,+\infty). The talk is based on a joint work with C. Esser and B. Vedel.