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ON THE MONOTONICITY OF THE MOMENTS OF VOLUMES OF RANDOM SIMPLICES

  • Benjamin Reichenwallner (a1) and Matthias Reitzner (a2)

Abstract

In a $d$ -dimensional convex body $K$ random points $X_{0},\ldots ,X_{d}$ 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 [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.

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