On the monotonicity of the moments of volumes of random simplices

Abstract

In a $d$-dimensional convex body $K$ random points $X_0,\dots ,X_d$ are chosen. Their convex hull is a random simplex. The expected volume of a random simplex is monotone under set inclusion, if $K\subset L$ 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, it is shown that moments of the volume of random simplices are in general not monotone under set inclusion.

References in corpus (1)

• On the monotonicity of the expected volume of a random simplex