Silhouette of a random polytope

Marc Glisse 1 Sylvain Lazard 2 Julien Michel 3 Marc Pouget 2
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : We consider random polytopes defined as the convex hull of a Poisson point process on a sphere in $\R^3$ 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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Submitted on : Thursday, March 17, 2016 - 11:06:36 AM
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Marc Glisse, Sylvain Lazard, Julien Michel, Marc Pouget. Silhouette of a random polytope. Journal of Computational Geometry, Carleton University, Computational Geometry Laboratory, 2016, 7 (1), pp.14. ⟨http://jocg.org/index.php/jocg/article/view/162⟩. ⟨10.20382/jocg.v7i1a5⟩. ⟨hal-01289699⟩

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