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Diffraction of stochastic point sets: Explicitly computable examples. (English) Zbl 1197.82053

Summary: Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of reasonable generality. The latter is based on the classical theory of point processes and the Palm distribution. Several pairs of autocorrelation and diffraction measures are discussed which show a duality structure analogous to that of the Poisson summation formula for lattice Dirac combs.

MSC:

82B31 Stochastic methods applied to problems in equilibrium statistical mechanics
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60K40 Other physical applications of random processes
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