Poisson polytopes

Details Poisson polytopes Poisson polytopes

2010-10-18

arxiv.org/abs/1010.3582v1

Annals of Probability 2010, Vol. 38, No. 4, 1507-1531

Mathematics

Probability

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

Scientific paper

10.1214/09-AOP514

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 $P$.

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