Central limit theorems for Gaussian polytopes

• 成果类型: Article
• 署名作者: Barany, Imre; Vu, Van
• 署名单位: Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of London; University College London; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000791
• 发表日期: 2007
• 页码: 1593-1621
• 关键词: convex-hull; points

摘要

Choose n random, independent points in R-d according to the standard normal distribution. Their convex hull K-n is the 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.