in this talk, we discuss the construction and invariance of the gibbs measure for a three-dimensional wave equation with a hartree-nonlinearity. in the first part of the talk, we construct the gibbs measure and examine its properties. we discuss the mutual singularity of the gibbs measure and the so-called gaussian free field. in contrast, the gibbs measure for one or two-dimensional wave equations is absolutely continuous with respect to the gaussian free field. in the second part of the talk, we discuss the probabilistic well-posedness of the corresponding nonlinear wave equation, which is needed in the proof of invariance. this was the first theorem proving the invariance of a singular gibbs measure for any dispersive equation.