Comparison of f-vectors of Random Polytopes to the Gaussian Distribution

2011/09/21 by Sang Du, Du, Sang, Mark Syvuk +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1109.4464

openalex publication_date 2011/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Choose n random, independent points in R^d according to a fixed distribution. The convex hull of these points is a random polytope. In some cases, central limit theorems have been proven for the components of f-vectors of random polytopes constructed in this and similar ways. In this paper, we provide numerical evidence that the components of the f-vectors of random polytopes generated according to five different distributions are approximately jointly Gaussian for large n.

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