Limit theorems for the diameter of a random sample in the unit ball

Mayer, Michael ; Molchanov, Ilya

In: Extremes, 2007, vol. 10, no. 3, p. 129-150

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    We prove a limit theorem for the maximum interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit d-dimensional ball for d≥2. The results are specialised for the cases when the points have spherical symmetric distributions, in particular, are uniformly distributed in the whole ball and on its boundary. Among other examples, we also give results for distributions supported by pointed sets, such as a rhombus or a family ofsegments