We extend a randomisation method, introduced by Burq-Lebeau on compact manifolds, to the case of the harmonic oscillator.  We construct measures, under concentration of measure type assumptions, on the support of which we prove optimal weighted Sobolev estimates on R^d. As an application we can prove almost sure global well posedness results for the nonlinear Schrödinger equation with harmonic potential. This is a joint work with Aurélien Poiret and Didier Robert.