Limit theorems for random polytopes with vertices on convex surfaces

We consider the random polytope Kn, defined as the convex hull of n points chosen independently and uniformly at random on the boundary of a smooth convex body in â"d. We present both lower and upper variance bounds, a strong law of large numbers, and a central limit theorem for the intrinsic volumes of Kn. A normal approximation bound from Stein's method and estimates for surface bodies are among the tools involved.