Poisson polytopes

Abstract

We prove the central limit theorem for the volume and the $f$-vector of the Poisson random polytope ${\Pi }_{\eta }$ in a fixed convex polytope $P\subset {\mathbb{R}}^d$. Here, ${\Pi }_{\eta }$ is the convex hull of the intersection of a Poisson process $X$ of intensity $\eta$ with $P$.

Published in at http://dx.doi.org/10.1214/09-AOP514 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)