01-139 Peter D. Hislop, Frederic Klopp

THE INTEGRATED DENSITY OF STATES FOR SOME RANDOM OPERATORS WITH NONSIGN DEFINITE POTENTIALS (97K, LaTex 2e) Apr 9, 01

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Abstract. We study the integrated density of states of random Anderson-type additive and multiplicative perturbations of deterministic background operators for which the single-site potential does not have a fixed sign. Our main result states that, under a suitable assumption on the regularity of the random variables, the integrated density of states of such random operators is locally H{\"o}lder continuous at energies below the bottom of the essential spectrum of the background operator for any nonzero disorder, and at energies in the unperturbed spectral gaps, provided the randomness is sufficiently small. The result is based on a proof of a Wegner estimate with the correct volume dependence. The proof relies upon the $L^p$-theory of the spectral shift function for $p \geq 1$ \cite{[CHN]}, and the vector field methods of \cite{[Klopp]}. We discuss the application of this result to \Schr\ operators with random magnetic fields and to band-edge localization.

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