Isotropic Zero Cells

In this chapter, we drop the stationarity assumption for the considered Poisson hyperplane processes, but we restrict ourselves to isotropic processes. The spherical directional distribution is allowed to depend on an additional parameter, which controls the distances of the hyperplanes from the origin. Thus, the intensity measure of the hyperplane process depends on this parameter and on the intensity. The focus of the first two sections is on the expected face numbers of the zero cell. Sections 4 and 5 deal with moments and the variance of the volume of the zero cell. Section 6 explores the asymptotic behavior of the intersection volume of the zero cell and a lower dimensional ball of fixed volume centered at the origin. The last section derives an exact formula for a second moment in the stationary case.