Original paper

Archiv der Mathematik

, Volume 82, Issue 1, pp 85-96

First online:

Volumes of symmetric random polytopes

  • M. W. MeckesAffiliated withDepartment of Mathematics, Case Western Reserve University Email author 

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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.

Mathematics Subject Classification (2000):

Primary 52A22 Secondary 60D05.