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Non-periodic systems with continuous diffraction measures

The present state of mathematical diffraction theory for systems with continuous spectral components is reviewed and extended. We begin with a discussion of various characteristic examples with singular or absolutely continuous diffraction, and then continue with a more general exposition of a systematic approach via stationary stochastic point processes. Here, the intensity measure of the Palm measure takes the role of the autocorrelation measure in the traditional approach. We furthermore introduce a `Palm-type' measure for general complex-valued random measures that are stationary and ergodic, and relate its intensity measure to the autocorrelation measure.