Distance measurements on processes of flats

Abstract

Distance measurements are useful tools in stochastic geometry. For a Boolean modelZin ℝd, the classical contact distribution functions allow the estimation of important geometric parameters ofZ. In two previous papers, several types of generalized contact distributions have been investigated and applied to stationary and nonstationary Boolean models. Here, we consider random setsZwhich are generated as the union sets of Poisson processesXofk-flats,k∈ {0, …,d-1}, and study distances from a fixed point or a fixed convex body toZ. In addition, we also consider the distances from a given flat or a flag consisting of flats to the individual members ofXand investigate the associated process of nearest points in the flats ofX. In particular, we discuss to which extent the directional distribution ofXis determined by this point process. Some of our results are presented for more general stationary processes of flats.