The limit distribution of the largest interpoint distance for distributions supported by a d-dimensional ellipsoid and generalizations. (11th January 2017)

• Record Type: Journal Article
• Authors: Schrempp, Michael
• Is Part Of: Advances in applied probability. Volume 48:Number 4(2016)
• Page Start: 1256
• Page End: 1270
• Publication Date: 2017-01-11
• Subjects: Maximum interpoint distance, -- geometric extreme value theory, -- Poisson process, -- uniform distribution in an ellipsoid; Primary 60D05, -- 60F05, -- Secondary 60G55, -- 60G70, -- 62E20; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2016.73
• Languages: English
• ISSNs: 0001-8678

Abstract

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.