On a multi-integral norm defined by weighted sums of log-concave random vectors

Nikos Skarmogiannis

Let $C$ and $K$ be centrally symmetric convex bodies in ${\mathbb{R}}^n$. We show that if $C$ is isotropic then \begin{equation*}\|{\bf t}\|_{C^s,K}=\int_{C}\cdots\int_{C}\Big\|\sum…