Advances in Applied Probability

The limit distribution of the largest interpoint distance for distributions supported by a d-dimensional ellipsoid and generalizations

Michael Schrempp

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Abstract

We study the asymptotic behaviour of the maximum interpoint distance of random points in a d-dimensional ellipsoid with a unique major axis. Instead of investigating only a fixed number of n points as n tends to ∞, we consider the much more general setting in which the random points are the supports of appropriately defined Poisson processes. Our main result covers the case of uniformly distributed points.

Article information

Source
Adv. in Appl. Probab., Volume 48, Number 4 (2016), 1256-1270.

Dates
First available in Project Euclid: 24 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.aap/1482548437

Mathematical Reviews number (MathSciNet)
MR3595774

Zentralblatt MATH identifier
1384.60044

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60F05: Central limit and other weak theorems
Secondary: 60G55: Point processes 60G70: Extreme value theory; extremal processes 62E20: Asymptotic distribution theory

Keywords
Maximum interpoint distance geometric extreme value theory Poisson process uniform distribution in an ellipsoid

Citation

Schrempp, Michael. The limit distribution of the largest interpoint distance for distributions supported by a d -dimensional ellipsoid and generalizations. Adv. in Appl. Probab. 48 (2016), no. 4, 1256--1270. https://projecteuclid.org/euclid.aap/1482548437


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