Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional poisson-voronoi tessellation and a poisson line process

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.