Limit theorems for the convex hull of random points in higher dimensions
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- by Irene Hueter
- Trans. Amer. Math. Soc. 351 (1999), 4337-4363
- DOI: https://doi.org/10.1090/S0002-9947-99-02499-X
- Published electronically: July 21, 1999
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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.References
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Bibliographic 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