Probability Theory and Related Fields

, Volume 79, Issue 3, pp 327–368

Limit theorems for convex hulls

  • Piet Groeneboom

DOI: 10.1007/BF00342231

Cite this article as:
Groeneboom, P. Probab. Th. Rel. Fields (1988) 79: 327. doi:10.1007/BF00342231


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.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Piet Groeneboom
    • 1
  1. 1.Faculty of Mathematics and InformaticsDelft University of TechnologyDelftThe Netherlands