On the shape of the convex hull of random points
- Cite this article as:
- Bárány, I. & Füredi, Z. Probab. Th. Rel. Fields (1988) 77: 231. doi:10.1007/BF00334039
Denote by En the convex hull of n points chosen uniformly and independently from the d-dimensional ball. Let Prob(d, n) denote the probability that En has exactly n vertices. It is proved here that Prob(d, 2d/2d-ɛ)→1 and Prob(d, 2d/2d(3/4)+ɛ)→0 for every fixed ɛ>0 when d→∞. The question whether En is a k-neighbourly polytope is also investigated.