Random convex hulls and the Stein method.
Preprint

The Stein method is engaged to prove asymptotic normality of the number N_n of vertices of the convex hull of a rotationally invariant sample of size n and to bound its normal approximation error. Examples that we consider include samples that are uniform in a d-ball, normal or drawn from exponentially decaying distributions in R^d for d \geq 2 satisfying certain conditions.