 02462 J.M. combes, P. D. Hislop, F. Klopp
 Local and Global Continuity of the Integrated Density of States
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Nov 14, 02

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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 infinitevolume
limit of the local eigenvalue counting function for the system restricted toa finitevolume region. For Schr\"odinger operators with random potentials,the eigenvalue counting function for the finitevolume system satisfies an estimate called a Wegner estimate. We present new local and globalinenergy Wegner estimates for random Schr\"odinger operators with Andersontype 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 $q > 1$.
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