Gaussian convex hull peels.
Preprint

Convex hull peeling of a finite point set provides a natural means to rank points in R^d and is appealing in multivariate statistics. The convex peels are consecutively obtained by repeatedly performing: (i) construct the convex hull of the point set and (ii) eliminate the points from the point set that span the hull. We examine the number N_n,i of vertices of the i-th convex hull peel of Poisson points with n expected points from a normal or other spherically symmetric distributions in R^d for d \geq 2 and show that the large n expectation and variance of N_n,i, for i \geq 1 below a certain threshold, remain constant as functions of i up to an error that depends on i. This sharply contrasts the behavior known for a uniform sample on a polygon or circular disk, where these two moments are strictly increasing functions of i.