On the Volume of the Zero Cell of a Class of Isotropic Poisson Hyperplane Tessellations. (September 2014)

• Record Type: Journal Article
• Authors: Hörrmann, Julia; Hug, Daniel
• Is Part Of: Advances in applied probability. Volume 46:Number 3(2014)
• Page Start: 622
• Page End: 642
• Publication Date: 2014-09
• Subjects: Poisson hyperplane tessellation, -- Poisson-Voronoi tessellation, -- zero cell, -- typical cell, -- variance, -- high dimensions; 60D05, -- 52A22; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1239/aap/1409319552
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract : We study a parametric class of isotropic but not necessarily stationary Poisson hyperplane tessellations in n -dimensional Euclidean space. Our focus is on the volume of the zero cell, i.e. the cell containing the origin. As a main result, we obtain an explicit formula for the variance of the volume of the zero cell in arbitrary dimensions. From this formula we deduce the asymptotic behaviour of the volume of the zero cell as the dimension goes to ∞.