Faces of Poisson-Voronoi mosaics

• 成果类型: Article
• 署名作者: Hug, Daniel; Schneider, Rolf
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology; University of Freiburg
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0294-7
• 发表日期: 2011
• 页码: 125-151
• 关键词: crofton cell

摘要

For a stationary Poisson-Voronoi tessellation in Euclidean d-space and for k is an element of {1, ... , d}, we consider the typical k-dimensional face with respect to a natural centre function. We express the distribution of this typical k-face in terms of a certain Poisson process of closed halfspaces in a k-dimensional space. Then we show that, under the condition of large inradius, the relative boundary of the typical k-face lies, with high probability, in a narrow spherical annulus.