Decorrelation Estimates for the Eigenlevels of the Discrete Anderson Model in the Localized Regime

The purpose of the present work is to establish decorrelation estimates for the eigenvalues of the discrete Anderson model localized near two distinct energies inside the localization region. In dimension one, we prove these estimates at all energies. In higher dimensions, the energies are required to be sufficiently far apart from each other. As a consequence of these decorrelation estimates, we obtain the independence of the limits of the local level statistics at two distinct energies.