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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Limit theorems for the convex hull of random points in higher dimensions
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by Irene Hueter PDF
Trans. Amer. Math. Soc. 351 (1999), 4337-4363 Request permission

Abstract:

We give a central limit theorem for the number $N_n$ of vertices of the convex hull of $n$ 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 $N_n$ 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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Additional Information
  • Irene Hueter
  • Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
  • Email: hueter@math.ufl.edu
  • Received by editor(s): December 2, 1998
  • Received by editor(s) in revised form: January 22, 1999
  • Published electronically: July 21, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 4337-4363
  • MSC (1991): Primary 52A22, 60D05
  • DOI: https://doi.org/10.1090/S0002-9947-99-02499-X
  • MathSciNet review: 1670156