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Limit theorems for random polytopes with vertices on convex surfaces
Published online by Cambridge University Press: 29 November 2018
Abstract
We consider the random polytope Kn, defined as the convex hull of n points chosen independently and uniformly at random on the boundary of a smooth convex body in ℝd. We present both lower and upper variance bounds, a strong law of large numbers, and a central limit theorem for the intrinsic volumes of Kn. A normal approximation bound from Stein's method and estimates for surface bodies are among the tools involved.
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- Copyright © Applied Probability Trust 2018
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