Transactions of the American Mathematical Society

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ISSN 1088-6850(e) ISSN 0002-9947(p)

Limit theorems for the convex hull of random points in higher dimensions

Author(s): Irene Hueter
Journal: Trans. Amer. Math. Soc. 351 (1999), 4337-4363.
MSC (1991): Primary 52A22, 60D05
Posted: July 21, 1999
MathSciNet review: 1670156
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Abstract: We give a central limit theorem for the number of vertices of the convex hull of independent and identically distributed random vectors, being sampled from a certain class of spherically symmetric distributions in $\mathbb{R}^d \; (d> 1),$ that includes the normal family. Furthermore, we prove that, among these distributions, the variance of exhibits the same order of magnitude as the expectation as $n \rightarrow \infty.$ The main tools are Poisson approximation of the point process of vertices of the convex hull and (sub/super)-martingales.

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