Department of
Applied
Mathematics

On the monotonicity of the expected complexity of a random polytope

Xavier Goaoc

INRIA

Abstract

A random polytope K(n) is usually defined as the convex hull of n points distributed independently and uniformly in a compact convex body K. The study of random polytopes goes back to Sylvester's "four points problem", which asked for the probability that four points chosen at random be in convex position. In this talk, I will present some old and some new results on the question of whether the expected complexity of K(n) is an increasing function of n.