  Quantum fluctuations of Bose-Einstein condensates trapped in disordered
lattices are studied by inhomogeneous Bogoliubov theory. Weak-disorder
perturbation theory is applied to compute the elastic scattering rate as well
as the renormalized speed of sound in lattices of arbitrary dimensionality.
Furthermore, analytical results for the condensate depletion are presented,
which are in good agreement with numerical data.
