Upper Estimates of the Density of States in one Dimension Interpolating between the Wegner and the Lifshitz Regime

We consider the density of states (DOS) of one-dimensional discrete random Schr?dinger operators with an uniformly distributed random potential. The Wegner estimates are uniform estimates of the DOS. They are expected to be inadequate close to the boundary of the spectrum, where Lifshitz behaviour should occur. We prove a result interpolating between the Wegner and the Lifshitz regime. Submitted: May 6, 2008. Accepted: January 20, 2009.