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VOLUMES OF SYMMETRIC RANDOM POLYTOPES
, 2003
"... Abstract. We consider the moments of the volume of the symmetric convex hull of independent random points in an ndimensional symmetric convex body. We calculate explicitly the second and fourth moments for n points when the given body is B n q (and all of the moments for the case q = 2), and derive ..."
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Abstract. We consider the moments of the volume of the symmetric convex hull of independent random points in an ndimensional symmetric convex body. We calculate explicitly the second and fourth moments for n points when the given body is B n q (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. 1.