ON THE MONOTONICITY OF THE MOMENTS OF VOLUMES OF RANDOM SIMPLICES

Abstract

In a d-dimensional convex body K random points X-0, . . . , X-d are chosen. Their convex hull is a random simplex. The expected volume of a random simplex is monotone under set inclusion if K. L implies that the expected volume of a random simplex in K is smaller than the expected volume of a random simplex in L. Continuing work of Rademacher [On the monotonicity of the expected volume of a random simplex. Mathematika 58 (2012), 77-91], it is shown that moments of the volume of random simplices are, in general, not monotone under set inclusion.