On the Intersection Density of Flat Processes

Stationary POISSON r-flat processes in the d-dimensional Euclidean space (d/2 ≦ r ≦ d − 1) induce a process of (2r − d)-flats each of which is the intersection of two r-flats of the original processes. The intensity of the induced (2r − d)-flat process is called intersection density of the original POISSON r-flat process. The problem of maximizing the intersection density for given intensity is considered. A new approach to earlier results of THOMAS and the author is presented.