Central limit theorems for Gaussian polytopes

Abstract

Choose $n$ random, independent points in ${\mathbb{R}}^d$ according to the standard normal distribution. Their convex hull $K_n$ is the {\sl Gaussian random polytope}. We prove that the volume and the number of faces of $K_n$ satisfy the central limit theorem, settling a well known conjecture in the field.

to appear in Annals of Probability