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

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.