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Mathematics > Combinatorics

arXiv:1806.04732 (math)
[Submitted on 12 Jun 2018]

Title:On the $1$-convexity of random points in the $d$-dimensional spherical layer

Authors:Sergey Sidorov
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Abstract:We consider the set of points chosen randomly, independently and uniformly in the $d$-dimensional spherical layer. A set of points is called $1$-convex if all its points are vertices of the convex hull of this set. In \cite{3} an estimate for the cardinality of the set of points for which this set is $1$-convex with probability close to $1$ was obtained. In this paper we obtain an improved estimate.
Comments: 4 pages
Subjects: Combinatorics (math.CO); Probability (math.PR)
Cite as: arXiv:1806.04732 [math.CO]
  (or arXiv:1806.04732v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1806.04732

Submission history

From: Sergey Sidorov [view email]
[v1] Tue, 12 Jun 2018 19:29:27 UTC (3 KB)
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