The simplex conjecture for random simplex volumes
Let KKK be a convex body in Rd\mathbb{R}^dRd, let TdT^dTd be a ddd-dimensional simplex, let p⩾1p\geqslant 1p⩾1, and let n⩾d+1n\geqslant d+1n⩾d+1. Write E∗p(K)\mathbb{E}^p_*(K)E∗p(K) and Enp(K)\mathbb{E}^p_n(K)Enp(K)…