  In this note, we give an overview of some results obtained in [3]. This
latter work is devoted to the study of the one-dimensional nonlinear
Schr{\"o}dinger equation with random initial conditions. Namely, we describe
the nonlinear evolution of Gaussian measures and we deduce global
well-posedness and scattering results for the corresponding nonlinear
Schr{\"o}dinger equation.
