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

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

2007-12-19

arxiv.org/abs/0712.3287v1

Mathematics

Dynamical Systems

49 pages

Scientific paper

10.1016/j.geomphys.2007.12.006

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.

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