The setting is an ergodic dynamical system
(X,μ) whose points are themselves uniformly discrete point sets
Λ in some space
and whose group action is that of translation of these point sets by the vectors of
. Steven Dworkin’s argument relates the diffraction of the typical point sets comprising
X to the dynamical spectrum of
X. In this paper we look more deeply at this relationship, particularly in the context of point processes.