Almost Sure Scattering for the Energy-Critical NLS with Radial Data Below H¹(ℝ⁴)

We prove almost sure global existence and scattering for the energy-critical nonlinear Schrödinger equation with randomized spherically symmetric initial data in Hs(ℝ4) with 5/6 \u3c s \u3c 1. We were inspired to consider this problem by the recent work of Dodson-Lührmann-Mendelson, which treated the analogous problem for the energy-critical wave equation