This paper reviews the mathematical connections among continuity of the diffraction spectrum, uniform vanishing of Fourier-Bohr coefficients, and consistent phase frequency.
Diffraction and Palm measure of point processes
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abstract
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^d, sets obtained by the ``cut-and-project'' method.
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Continuous diffraction spectrum and the uniform vanishing of Fourier--Bohr coefficients
This paper reviews the mathematical connections among continuity of the diffraction spectrum, uniform vanishing of Fourier-Bohr coefficients, and consistent phase frequency.