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)

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• Interaction of Poisson hyperplane processes and convex bodies
• A central limit theorem for random disc-polygons in smooth convex discs
• Convex curves and a Poisson imitation of lattices