Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 48, Number 4 (2016), 1256-1270.
The limit distribution of the largest interpoint distance for distributions supported by a d-dimensional ellipsoid and generalizations
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.
Adv. in Appl. Probab., Volume 48, Number 4 (2016), 1256-1270.
First available in Project Euclid: 24 December 2016
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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