J.-M. combes, P. D. Hislop, F. Klopp
Local and Global Continuity of the Integrated Density of States
(53K, LaTex 2e)
ABSTRACT. The integrated density of states (IDS) $N(E)$ is the distribution function of a nonnegative measure $\nu$, 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 toa finite-volume region. For Schr\"odinger 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 Schr\"odinger operators with Anderson-type random potentials.
These estimates are strong enough to imply that the DOS measure is
absolutely continuous with a density in $L^q_{loc} ( \R)$, for any $1 \leq q < \infty$. The IDS is also proved to be locally or globally H\"older continuous with H\"older exponent $1 / q$, for any $q > 1$.