Christof Kuelske
Universal bounds on the selfaveraging
of random diffraction measures
(276K, Postscript)
ABSTRACT. We consider diffraction at random point scatterers on general discrete
point sets in R^n, 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.