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

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• 作者：Michael Mayer and Ilya Molchanov
• 关键词：Convex hull ; Extreme value ; Interpoint distance ; Poisson process ; Random diameter ; Random polytope
• 刊名：Extremes
• 出版年：2007
• 出版时间：September, 2007
• 年：2007
• 卷：10
• 期：3
• 页码：129-150
• 全文大小：489.6 KB

文摘

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.