Abstract: In this talk I will define and discuss some probability measures in infinite dimensions, which play an important role in (S)PDE, in Quantum Field Theory and for Bose-Einstein condensates. Those are Gibbs measures associated with the Gross-Pitaevskii and Hartree energies. In dimensions larger than or equal to 2, the measures are concentrated on distribution spaces, and the nonlinear term has to be renormalized. I will then present some recent results in collaboration with Phan Thanh Nam and Nicolas Rougerie about the derivation of these measures from many-body quantum mechanics in a mean-field type limit