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Volumes of symmetric random polytopes

Mark W. Meckes
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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 $B_q^n$ (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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Mark W. Meckes. 2003-05-28. Volumes of symmetric random polytopes. https://arxiv.org/abs/math/0305410

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