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arXiv · 1010.3582

Poisson polytopes

Imre Bárány·Matthias Reitzner
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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 $P$.

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Imre Bárány, Matthias Reitzner. 2010-10-18. Poisson polytopes. https://doi.org/10.1214/09-aop514

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