A Duality for Poisson Flats
Rolf Schneider · Advances in Applied Probability · 1999
In keeping with the intersection density of a stationary Poisson process of r -flats in Euclidean d -space, where r ≥ d /2, we introduce a notion of closeness, called proximity, for such processes if r < d /2. It is shown that the two notions are connected by a duality: the proximity of a stationary Poisson r -flat process is, up to a constant factor, the intersection density of a certain unique stationary Poisson ( d − r )-flat process.