2 problems

Let $K\subset\mathbb R^n$ be an origin-symmetric convex body, let $GL_n$ denote the group of invertible linear transformations of $\mathbb R^n$, and let $\ell(K)$ be the product fu…

Let $K\subset\mathbb{R}^d$ be a symmetric convex body, let $X$ be uniformly distributed on $K$, and let $\Sigma$ be the covariance matrix of $X$, with entries … Write $\|\Sigma\|$…