Silhouette of a random polytope

Marc Glisse, Sylvain Lazard, Julien Michel, Marc Pouget

Abstract


We consider random polytopes defined as the convex hull of a Poisson point process on a sphere in $\mathbb{R}^3$ such that its average number of points is $n$. We show that the expectation over all such random polytopes of the maximum size of their silhouettes viewed from infinity is $\Theta(\sqrt{n})$.


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DOI: http://dx.doi.org/10.20382/jocg.v7i1a5

ISSN: 1920-180X