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.
- Volumes of symmetric random polytopes
Archiv der Mathematik
Volume 82, Issue 1 , pp 85-96
- Cover Date
- Print ISSN
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- Primary 52A22
- Secondary 60D05.
- M. W. Meckes (1)
- Author Affiliations
- 1. Department of Mathematics, Case Western Reserve University, 44106, Cleveland, Ohio, USA