Distance measurements on processes of flats

• Published in: Advances in applied probability 2003-03, Vol.35 (1), p.70-95
• Main Authors: Hug, Daniel, Last, Günter, Weil, Wolfgang
• Format: Article
• Language: English
• ISSN: 0001-8678; 1475-6064
• DOI: 10.1017/S000186780001209X

Distance measurements are useful tools in stochastic geometry. For a Boolean model Z in ℝ d , the classical contact distribution functions allow the estimation of important geometric parameters of Z . 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 sets Z which are generated as the union sets of Poisson processes X of k -flats, k ∈ {0, …, d -1}, and study distances from a fixed point or a fixed convex body to Z . In addition, we also consider the distances from a given flat or a flag consisting of flats to the individual members of X and investigate the associated process of nearest points in the flats of X . In particular, we discuss to which extent the directional distribution of X is determined by this point process. Some of our results are presented for more general stationary processes of flats.