## Dworkin's argument revisited: point processes, dynamics, diffraction, and correlations

Deng, Xinghua
Moody, Robert V.
##### Description
The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently the 2-point correlations) usually cannot determine the dynamics entirely, but we prove that knowledge of all the higher correlations (2-point, 3-point, ...) does. A square-mean form of the Bombieri-Taylor conjecture is proved. A quantitative relation between autocorrelation, diffraction, and epsilon dual characters is derived. Most results of the paper are proved in the setting of multi-colour points and assignable scattering strengths.
Comment: 49 pages
##### Keywords
Mathematics - Dynamical Systems, Mathematical Physics, 37A50, 37A60, 60G55