How far can the geometric median be from the mean under variance normalization? – mathoverflow.net

Let $X$ be a random variable in $\mathbb{R}^d$ with law $\mu$. We denote by $\mathcal{P}(\mathbb{R}^d)$ the set of all Borel probability measures on $\mathbb{R}^d$. Assume that $\mu \in ...