Volumes of symmetric random polytopes
- Cite this article as:
- Meckes, M. Arch. Math. (2004) 82: 85. doi:10.1007/s00013-003-4808-8
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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, as \( n \rightarrow \infty \) , of the expected volume of a random simplex in those bodies.