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Diffraction of Weighted Lattice Subsets
"... A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniform lattice Dirac comb, a ..."
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A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniform lattice Dirac comb, and its diraction measure is periodic, with the dual lattice as lattice of periods. This statement remains true in the setting of a locally compact Abelian group that is also compact.
Diffraction of stochastic point sets: Explicitly computable examples
 COMMUN. MATH. PHYS
, 2009
"... Stochastic point processes relevant to the theory of longrange 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 ..."
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Cited by 16 (11 self)
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Stochastic point processes relevant to the theory of longrange 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.
Which distributions of matter diffract? Some answers
, 2002
"... This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a distribution has pure point diffraction. We explain how a cu ..."
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Cited by 10 (3 self)
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This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a distribution has pure point diffraction. We explain how a cut and project scheme naturally appears in this context and then turn our attention to the special situation of model sets and lattice substitution systems. As an example, we analyse the paperfolding sequence. In the last part, we summarize some aspects of stochastic point sets, with focus both on structure and diffraction.
Diffraction spectrum of lattice gas models above Tc
"... ABSTRACT. The diffraction spectra of lattice gas models on Z d with finiterange ferromagnetic twobody interactions above Tc or with certain rates of decay of the potential are considered. We show that these diffraction spectra almost surely exist, are Z dperiodic and consist of a pure point part ..."
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Cited by 7 (5 self)
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ABSTRACT. The diffraction spectra of lattice gas models on Z d with finiterange ferromagnetic twobody interactions above Tc or with certain rates of decay of the potential are considered. We show that these diffraction spectra almost surely exist, are Z dperiodic and consist of a pure point part and an absolutely continuous part with continuous density. 1.
Diffraction of stochastic point sets: Exactly solvable examples
, 2008
"... Abstract. Stochastic point sets are considered that display a diffraction spectrum of mixed type, with special emphasis on explicitly computable cases together with a unified approach of reasonable generality. Several pairs of autocorrelation and diffraction measures are discussed which show a duali ..."
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Cited by 2 (1 self)
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Abstract. Stochastic point sets are considered that display a diffraction spectrum of mixed type, with special emphasis on explicitly computable cases together with a unified approach of reasonable generality. Several pairs of autocorrelation and diffraction measures are discussed which show a duality structure that may be viewed as analogues of the Poisson summation formula for lattice Dirac combs. 1.