Archiv der Mathematik

, Volume 82, Issue 1, pp 85–96

Volumes of symmetric random polytopes

Original paper

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, as \( n \rightarrow \infty \) , of the expected volume of a random simplex in those bodies.

Mathematics Subject Classification (2000):

Primary 52A22 Secondary 60D05. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsCase Western Reserve UniversityClevelandUSA

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