Concentration between Lévy's inequality and the Poincaré inequality for log-concave densities

Erez Buchweitz

Given a suitably normalized $X\in {\mathbb{R}}^n$ we observe that the function $\theta \mapsto \mathbb{E}|X\cdot \theta |$, defined for $\theta \in S^{n-1}$, admits surprisingly strong concentration far…