Sharp inequalities for the mean distance of random points in convex bodies

Gilles Bonnet, Anna Gusakova, Christoph Thäle +1

For a convex body $K\subset {\mathbb{R}}^d$ the mean distance $\Delta (K)=\mathbb{E}|X_1-X_2|$ is the expected Euclidean distance of two independent and uniformly distributed random points…