Generalized contact distributions of inhomogeneous Boolean models

The main purpose of this work is to study and apply generalized contact distributions of (inhomogeneous) Boolean models Z with values in the extended convex ring. Given a convex body L ⊂ Rd and a gauge body B ⊂ Rd such a generalized contact distribution is the conditional distribution of the random vector (dB(L,Z), uB(L,Z), pB(L,Z), lB(L,Z)) given that Z ∩L = ∅, where Z is a Boolean model, dB(L,Z) is the distance of L from Z with respect to B, pB(L,Z) is the boundary point in L realizing this distance (if it exists uniquely), uB(L,Z) is the corresponding boundary point of B (if it exists uniquely) and lB(L, ·) may be taken from a large class of locally defined functionals. In particular, we pursue the question to which extent the spatial density and the grain distribution underlying an inhomogeneous Boolean model Z are determined by the generalized contact distributions of Z.