Diffraction and Palm measure of point processes

Using the Palm measure notion, we prove the existence of the diffraction measure of all stationary and ergodic point processes. We get precise expressions of those measures in the case of specific processes : stochastic subsets of Z, sets obtained by the “cut-and-project” method. From a physical point of view, the diffraction of X rays by a material is a way of studying its microscopic structure. We remind the mathematical formalism of diffraction theory (Hof [2]). Let χ be a a locally finite subset of R (physically, each point of χ is the center of an atom). The autocorrelation γR is defined by