Central limit theorems for Gaussian polytopes

2006/10/05 by Imre Bárány, Barany, I., Van H. Vu +1
Agricultural and Biological Sciences · Mathematics · Medicine · #Animal Diversity and Health Studies #Combinatorics (math.CO) #FOS: Mathematics #Pharmacological Effects of Medicinal Plants #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.math/0610192

openalex publication_date 2006/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Choose n random, independent points in \R^d according to the standard normal distribution. Their convex hull K_n is the \sl Gaussian random polytope. We prove that the volume and the number of faces of K_n satisfy the central limit theorem, settling a well known conjecture in the field.

Related

• Central limit theorems for random polytopes in a smooth convex set
• Central limit theorems for random boundary polytopes
• Comparison of f-vectors of Random Polytopes to the Gaussian Distribution
• Random polytopes: central limit theorems for intrinsic volumes
• Limit theorems for random polytopes with vertices on convex surfaces