** Rafik Imekraz (La Rochelle)**

**About uniform convergence of random series of radial eigenfunctions.**

en collaboration avec Pierre Brun et Guillaume Poly

We consider random linear series of the zonal eigenfunctions on the
Euclidean space. We aim to get a necessary and sufficient condition of
continuity. Such a problem has been posed by Ayache and Tzvetkov and is
motivated by understanding analogues of a famous problem about random
linear trigometric series (solved by Dudley and Fernique in the 60's).
We shall give a solution which turns out to be linked with a
Paley-Littlewood characterization of the so-called "pointwise Hölder"
regularity.