Limit theorems for the convex hull of random points in higher dimensions. Transactions of the American Mathematical Society, 351, 4337-4363 (1999)

We give a central limit theorem for the number N_n of vertices of the convex hull of n independent and identically distributed random vectors, being sampled from a certain class of spherically symmetric distributions in R^d (d > 1), that includes the normal family. Furthermore, we prove that, among these distributions, the variance of N_n exhibits the same order of magnitude as the expectation as n approaches infinity. The main tools are Poisson approximation of the point process of vertices of the convex hull and (sub/super)-martingales.