The Annals of Applied Probability

On the Asymptotic Distribution of the Area Outside a Random Convex Hull in a Disk

Tailen Hsing

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 4, Number 2 (1994), 478-493.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005069

Digital Object Identifier
doi:10.1214/aoap/1177005069

Mathematical Reviews number (MathSciNet)
MR1272736

Zentralblatt MATH identifier
0806.60004

JSTOR
links.jstor.org

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60F05: Central limit and other weak theorems

Keywords
Asymptotic distribution convex hull point processes

Citation

Hsing, Tailen. On the Asymptotic Distribution of the Area Outside a Random Convex Hull in a Disk. Ann. Appl. Probab. 4 (1994), no. 2, 478--493. doi:10.1214/aoap/1177005069. https://projecteuclid.org/euclid.aoap/1177005069


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