Moment estimates for convex measures

Radosław Adamczak, Olivier Guédon, Rafał Latała +4

Let $p\ge 1$, $\eps >0$, $r\geq (1+\eps) p$, and $X$ be a $(-1/r)$-concave random vector in ${\mathbb{R}}^n$ with Euclidean norm $|X|$. We prove that $(\E |X|^{p})^{1/{p}}\leq c (C(\eps) \E…