WIAS Preprint No. 676, (2001)

Universal bounds on the selfaveraging of random diffraction measures



Authors

  • Külske, Christof

2010 Mathematics Subject Classification

  • 78A45 82B44 60F10 82B20

2008 Physics and Astronomy Classification Scheme

  • 61.10.Dp 05.50.+q 02.50.Cw

Keywords

  • Diffraction theory, random scatterers, random point sets, quasicrystals, large deviations, cluster expansions

Abstract

We consider diffraction at random point scatterers on general discrete point sets in ℝν, 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.

Appeared in

  • Probab. Theory Related Fields, 126 (2003), pp. 29-50

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