On the SoS Certifiability of Log-Concave Distributions

Aleksandr Storozhenko

We prove that for every isotropic log-concave distribution $P$ on ${\mathbb{R}}^d$ and every even $m\ge 2$, the polynomial $(Cm{)}^m\Vert v{\Vert }_2^m-{\mathbb{E}}_{X\sim P}⟨X,v{⟩}^m$…