Volumes of symmetric random polytopes

Details Volumes of symmetric random polytopes Volumes of symmetric random polytopes

2003-05-28

arxiv.org/abs/math/0305410v1

Arch. Math. 82 (2004) no. 1, 85-96

Mathematics

Metric Geometry

AMS-LaTeX

Scientific paper

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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