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Universal bounds on the selfaveraging of random diffraction measures.

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Názov: Universal bounds on the selfaveraging of random diffraction measures.
Autori: Külske, Christof
Zdroj: Probability Theory & Related Fields; 2003, Vol. 126 Issue 1, p29, 22p
Predmety: DIFFRACTION patterns, RANDOM measures, MATHEMATICAL functions
Abstrakt: We consider diffraction at random point scatterers on general discrete point sets in ℝ[sup ν] , restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence of the random scattering measures applied to an observable towards its mean, when the finite volume tends to infinity. We give an explicit universal large deviation upper bound that is exponential in the number of scatterers. The rate is given in terms of a universal function that depends on the point set only through the minimal distance between points, and on the observable only through a suitable Sobolev-norm. Our proof uses a cluster expansion and also provides a central limit theorem. [ABSTRACT FROM AUTHOR]
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Databáza: Complementary Index
Popis
Abstrakt:We consider diffraction at random point scatterers on general discrete point sets in ℝ[sup ν] , restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence of the random scattering measures applied to an observable towards its mean, when the finite volume tends to infinity. We give an explicit universal large deviation upper bound that is exponential in the number of scatterers. The rate is given in terms of a universal function that depends on the point set only through the minimal distance between points, and on the observable only through a suitable Sobolev-norm. Our proof uses a cluster expansion and also provides a central limit theorem. [ABSTRACT FROM AUTHOR]
ISSN:01788051