Comparison of f-vectors of Random Polytopes to the Gaussian Distribution

Abstract

Choose n random, independent points in R^d according to a fixed distribution. The convex hull of these points is a random polytope. In some cases, central limit theorems have been proven for the components of f-vectors of random polytopes constructed in this and similar ways. In this paper, we provide numerical evidence that the components of the f-vectors of random polytopes generated according to five different distributions are approximately jointly Gaussian for large n.