Title: Almost sure scattering for the energy-critical NLS with radial data below $H^1(\mathbb{R}^4)$,
Abstract: We prove almost sure global existence and scattering for the energy-critical
nonlinear Schrödinger equation with randomized spherically symmetric initial
data in $H^s(\mathbb{R}^4)$ with $\frac56<s<1$. 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.