  In the focus of our attention is the asymptotic properties of the sequence of
convex hulls which arise as a result of a peeling procedure applied to the
convex hull generated by a Poisson point process. Processes of the considered
type are tightly connected with empirical point processes and stable random
vectors. Results are given about the limit shape of the convex hulls in the
case of a discrete spectral measure. We give some numerical experiments to
illustrate the peeling procedure for a more large class of Poisson point
processes.
