Local and Global Continuity of the Integrated Density of States

The integrated density of states (IDS) N(E) is the distribution function of a nonnegative measure ν, the density of states measure (DOS). This measure usually obtained as the weak infinite-volume limit of the local eigenvalue counting function for the system restricted to a finite-volume region. For Schrödinger operators with random potentials, the eigenvalue counting function for the finite-volume system satisfies an estimate called a Wegner estimate. We present new local and global-in-energy Wegner estimates for random Schrödinger operators with Anderson-type random potentials. These estimates are strong enough to imply that the DOS measure is absolutely continuous with a density in L loc (R), for any 1 ≤ q < ∞. The IDS is also proved to be locally or globally Hölder continuous with Hölder exponent 1/q, for any q > 1.