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

Date
Authors
Deng, Xinghua
Moody, Robert V.
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
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
Citation
Collections