Abstract
We study lower-dimensional volume-weighted typical faces of a stationary Poisson hyperplane tessellation in d-dimensional Euclidean space. After showing how their distribution can be derived from that of the zero cell, we obtain sharp lower and upper bounds for the expected vertex number of the volume-weighted typical k-face (k=2,…,d). The bounds are respectively attained by parallel mosaics and by isotropic tessellations. We conclude with a remark on expected face numbers and expected intrinsic volumes of the zero cell.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference13 articles.
1. Zonoide und verwandte Klassen konvexer K�rper
2. Ensembles fermés aléatoires, ensembles semi-markoviens et polyèdres poissoniens
3. Stochastic and Integral Geometry
4. [8] Miles R. E. (1961). Random polytopes: the generalisation to n dimensions of the intervals of a Poisson process. Doctoral Thesis, Cambridge University.
5. [1] Baumstark V. and Last G. (2007). Gamma distributions for stationary Poisson flat processes. Submitted.
Cited by
14 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献