Diffraction of stochastic point sets: Explicitly computable examples

Abstract

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.

50 pages, 1 figure; revised and expanded version

References in corpus (4)

• Pure Point spectrum for measure dynamical systems on locally compact Abelian groups
• A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns
• Dworkin's argument revisited: point processes, dynamics, diffraction, and correlations
• Absence of singular continuous diffraction for discrete multi-component particle models

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