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.