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

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