Random polytopes: central limit theorems for intrinsic volumes

2017/02/03 by Christoph Thaele, Thaele, Christoph, Nicola Turchi +3
Computer Science · Mathematics · #52A22 #60D05 #60F05 #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1702.01069

openalex publication_date 2017/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Short and transparent proofs of central limit theorems for intrinsic volumes of random polytopes in smooth convex bodies are presented. They combine different tools such as estimates for floating bodies with Stein's method from probability theory.

Related

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• Limit theorems for random polytopes with vertices on convex surfaces
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• Central limit theorems for Gaussian polytopes