Limit theorems for the diameter of a random sample in the unit ball |
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Authors: | Michael Mayer Ilya Molchanov |
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Institution: | (1) Department of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland |
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Abstract: | 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 of segments.
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Keywords: | Convex hull Extreme value Interpoint distance Poisson process Random diameter Random polytope |
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