Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations

Abstract

We consider the defocusing nonlinear wave equations (NLW) on the two-dimensional torus. In particular, we construct invariant Gibbs measures for the renormalized so-called Wick ordered NLW. We then prove weak universality of the Wick ordered NLW, showing that the Wick ordered NLW naturally appears as a suitable scaling limit of non-renormalized NLW with Gaussian random initial data.