Random points on the boundary of smooth convex bodies

Reitzner, Matthias

doi:10.1090/S0002-9947-02-02962-8

Random points on the boundary of smooth convex bodies
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Trans. Amer. Math. Soc. 354 (2002), 2243-2278 Request permission

Abstract:

The convex hull of $n$ independent random points chosen on the boundary of a convex body $K \subset \mathbb {R}^d$ according to a given density function is a random polytope. The expectation of its $i$–th intrinsic volume for $i=1, \dots , d$ is investigated. In the case that the boundary of $K$ is sufficiently smooth, asymptotic expansions for these expected intrinsic volumes as $n \to \infty$ are derived.

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