  The purpose of this article is to construct global solutions for some
super-crtical Schrodinger equations using the theory of random data introduced
by N.Burq and N.Tzvetkov. We begin our study by the cubic equation in three
dimension. Thanks to the lens transform, it suffices to study a local theory
for the Schr\"odinger equations with harmonic potential and we can establish
Bourgain type bilinear estimates for the harmonic oscillator. Then, we explain
how we can generalize this result in all dimensions.
