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Limit theorems for convex hulls
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  • Published: October 1988

Limit theorems for convex hulls

  • Piet Groeneboom1 

Probability Theory and Related Fields volume 79, pages 327–368 (1988)Cite this article

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Abstract

It is shown that the process of vertices of the convex hull of a uniform sample from the interior of a convex polygon converges locally, after rescaling, to a strongly mixing Markov process, as the sample size tends to infinity. The structure of the limiting Markov process is determined explicitly, and from this a central limit theorem for the number of vertices of the convex hull is derived. Similar results are given for uniform samples from the unit disk.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Delft University of Technology, Julianalaan, 132, 2628 BL, Delft, The Netherlands

    Piet Groeneboom

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  1. Piet Groeneboom
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Groeneboom, P. Limit theorems for convex hulls. Probab. Th. Rel. Fields 79, 327–368 (1988). https://doi.org/10.1007/BF00342231

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  • Received: 14 April 1987

  • Revised: 26 May 1988

  • Issue Date: October 1988

  • DOI: https://doi.org/10.1007/BF00342231

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Keywords

  • Hull
  • Stochastic Process
  • Probability Theory
  • Limit Theorem
  • Convex Hull
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