Variance asymptotics for random polytopes in smooth convex bodies

• 成果类型: Article
• 署名作者: Calka, Pierre; Yukich, J. E.
• 署名单位: Universite de Rouen Normandie; Lehigh University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0484-1
• 发表日期: 2014
• 页码: 435-463
• 关键词: CENTRAL LIMIT-THEOREMS; hulls; set

摘要

Let be a smooth convex set and let be a Poisson point process on of intensity . The convex hull of is a random convex polytope . As , we show that the variance of the number of -dimensional faces of , when properly scaled, converges to a scalar multiple of the affine surface area of . Similar asymptotics hold for the variance of the number of -dimensional faces for the convex hull of a binomial process in K.