Volumes of symmetric random polytopes

2003/05/28 by Mark W. Meckes
Mathematics · #math.MG #math.PR #msc:52A22 #msc:60D05

paper · pdf

published as Arch. Math. 82 (2004) no. 1, 85-96 · AMS-LaTeX

arxiv created 2003/05/28 · arxiv updated 2009/11/30

Abstract

We consider the moments of the volume of the symmetric convex hull of independent random points in an n-dimensional symmetric convex body. We calculate explicitly the second and fourth moments for n points when the given body is B_qⁿ (and all of the moments for the case q = 2), and derive from these the asymptotic behavior of the expected volume of a random simplex in those bodies.

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