Limit theorems for convex hulls
- Cite this article as:
- Groeneboom, P. Probab. Th. Rel. Fields (1988) 79: 327. doi:10.1007/BF00342231
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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.