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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… Click to show full abstract
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.
Keywords:
polytopes vertices;
theorems random;
limit theorems;
vertices convex;
random polytopes;
convex surfaces
Journal Title: Advances in Applied Probability
Year Published: 2018
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Journal Title: Advances in Applied Probability
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!