 01139 Peter D. Hislop, Frederic Klopp
 THE INTEGRATED DENSITY OF STATES FOR SOME RANDOM OPERATORS WITH NONSIGN DEFINITE POTENTIALS
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Apr 9, 01

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Abstract. We study the integrated density of states of random Andersontype additive and
multiplicative perturbations of deterministic background operators for
which the singlesite 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 bandedge localization.
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