Poisson flats in Euclidean spaces Part II: Homogeneous Poisson flats and the complementary theorem

Abstract

Part I [21] treated the case of a finite number of independent random uniform s-flats in an ‘admissible’ subset of E d (s = 0, · · ·, d − 1). In this second part, the natural and fruitful ‘Poisson extension’ to a ‘countable number of independent random uniform s-flats in E d itself” is considered. It is worth mentioning at the outset that to have read Part I is not a prerequisite for reading the present paper. Although results of that part are often applied here, they serve only in an auxiliary capacity, thereby allowing the main thread of the theory to be developed without interruption.