Band edge localization and the density of states for acoustic and electromagnetic waves in random media

The propagation of sound waves and electromagnetic radiation in a backgroun d medium is strongly influenced by the addition of random scatterers. We st udy random perturbations of a background medium which has a spectral gap in its permissible energy spectrum. We prove that the randomness localizes wa ves at energies near the band edges of the spectral gap of the background m edium. The perturbations of the dielectric function or the sound speed are described by Anderson-type potentials, which include random displacements f rom the equilibrium positions which model thermal vibrations. The waves wit h energies near the band edges are almost-surely exponentially localized. W e prove a Wegner estimate valid at all energies in the spectral gap of the unperturbed operator. It follows that the integrated density of states is L ipschitz continuous at energies in the unperturbed spectral gaps. (C) Elsev ier, Paris.