On peeling procedure applied to a Poisson point process

TL;DR

This paper investigates the asymptotic behavior of convex hulls formed by peeling procedures on Poisson point processes, revealing limit shapes and illustrating the process through numerical experiments.

Contribution

It provides new insights into the limit shapes of convex hulls from Poisson processes with discrete spectral measures and demonstrates the peeling procedure's properties.

Findings

Limit shape characterized for discrete spectral measures

Numerical experiments illustrate peeling procedure

Connections with empirical processes and stable vectors

Abstract

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.