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May, 1994 On the Asymptotic Distribution of the Area Outside a Random Convex Hull in a Disk
Tailen Hsing
Ann. Appl. Probab. 4(2): 478-493 (May, 1994). DOI: 10.1214/aoap/1177005069

Abstract

The asymptotic distribution of the area $V_n$ outside the convex hull of $n$ i.i.d. points uniformly distributed on the two-dimensional unit disk is studied. The asymptotic variance of $V_n$ is found to be of the order $n^{-5/3}$, and the asymptotic distribution of $V_n$ is shown to be normal. The results are obtained by carefully analyzing the strength of dependence between sample points at different locations close to the boundary of the unit disk.

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Tailen Hsing. "On the Asymptotic Distribution of the Area Outside a Random Convex Hull in a Disk." Ann. Appl. Probab. 4 (2) 478 - 493, May, 1994. https://doi.org/10.1214/aoap/1177005069

Information

Published: May, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0806.60004
MathSciNet: MR1272736
Digital Object Identifier: 10.1214/aoap/1177005069

Subjects:
Primary: 60D05
Secondary: 60F05

Keywords: asymptotic distribution , Convex hull , Point processes

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.4 • No. 2 • May, 1994
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