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We study the Cauchy problem for the radial energy critical nonlinear waveequation in three dimensions. Our main result proves almost sure scattering forradial initial data below the energy space. In order to preserve the sphericalsymmetry of the initial data, we construct a radial randomization that is basedon annular Fourier multipliers. We then use a refined radial Strichartzestimate to prove probabilistic Strichartz estimates for the random linearevolution. The main new ingredient in the analysis of the nonlinear evolutionis an interaction flux estimate between the linear and nonlinear components ofthe solution. We then control the energy of the nonlinear component by a triplebootstrap argument involving the energy, the Morawetz term, and the interactionflux estimate.

Almost sure scattering for the radial energy critical nonlinear wave equation in three dimensions