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The limit distribution of the largest interpoint distance for distributions supported by a d-dimensional ellipsoid and generalizations
Part of
Michael Schrempp
Journal:

Advances in Applied Probability / Volume 48 / Issue 4 / December 2016

Published online by Cambridge University Press:

11 January 2017, pp. 1256-1270

Print publication:

December 2016
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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.

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