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On the area and perimeter of a random convex hull in a bounded convex set

Abstract.

Suppose K is a compact convex set in ℝ2 and X i , 1≤in, is a random sample of points in the interior of K. Under general assumptions on K and the distribution of the X i we study the asymptotic properties of certain statistics of the convex hull of the sample.

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Received: 24 July 1996/Revised version: 24 February 1998

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Bräker, H., Hsing, T. On the area and perimeter of a random convex hull in a bounded convex set. Probab Theory Relat Fields 111, 517–550 (1998). https://doi.org/10.1007/s004400050176

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  • Mathematics Subject Classification (1991): 60D05
  • 60F05