Limit theory for the first layers of the random convex hull peeling in the unit ball

• 成果类型: Article
• 署名作者: Calka, Pierre; Quilan, Gauthier
• 署名单位: Universite de Rouen Normandie
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01224-6
• 发表日期: 2023
• 页码: 1037-1091
• 关键词: variance asymptotics; random polytopes; normal approximation; intrinsic volumes; MONOTONICITY

摘要

The convex hull peeling of a point set is obtained by taking the convex hull of the set and repeating iteratively the operation on the interior points until no point remains. The boundary of each hull is called a layer. We study the number of k-dimensional faces and the outer defect intrinsic volumes of the first layers of the convex hull peeling of a homogeneous Poisson point process in the unit ball whose intensity goes to infinity. More precisely we provide asymptotic limits for their expectation and variance as well as a central limit theorem. In particular, the growth rates do not depend on the layer.