Abstract
In this paper, we give an explicit integral expression for the joint distribution of the number and the respective positions of the sides of the typical cell 𝒞 of a two-dimensional Poisson-Voronoi tessellation. We deduce from it precise formulae for the distributions of the principal geometric characteristics of 𝒞 (area, perimeter, area of the fundamental domain). We also adapt the method to the Crofton cell and the empirical (or typical) cell of a Poisson line process.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference23 articles.
1. Random Subdivisions of Space into Crystals
2. Spatial Tessellations
3. Calka P. (2002). The explicit expression of the distribution of the number of sides of the typical Poisson–Voronoi cell. Preprint, 02-02 LaPCS, Université Claude Bernard Lyon 1.
4. Random Distribution of Lines in a Plane
5. Estimates for distributions of the Voronoi polygon's geometric characteristics
Cited by
42 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