Point-Shift Foliation of a Point Process

الأصل · EN

A point-shift F maps each point of a point process Φ to some point of Φ. For all translation invariant point-shifts F, the F-foliation of Φ is a partition of the support of Φ which is the discrete analogue of the stable manifold of F on Φ. It is first shown that foliations lead to a classification of the behavior of point-shifts on point processes. Both qualitative and quantitative properties of foliations are then established. It is shown that for all point-shifts F, there exists a point-shift F, the orbits of which are the F-foils of Φ, and which are measure-preserving. The foils are not always stationary point processes. Nevertheless, they admit relative intensities with respect to one another.