Dirk Hundertmark, Rowan Killip, Shu Nakamura, Peter Stollmann, and Ivan Veselic'
Bounds on the spectral shift function and the density of states
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ABSTRACT. We study spectra of Schroedinger operators on $\RR^d$. First we consider a pair of operators which differ
by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay
of the singular values $\mu_n$ of the difference of the semigroups as $n\to \infty$ and
deduce bounds on the spectral shift function of the pair of operators.
Thereafter we consider alloy type random Schroedinger operators. The single site potential $u$ is assumed to
be non-negative and of compact support. The distributions of the random coupling constants are assumed to be
Hoelder continuous. Based on the estimates for the spectral shift function, we prove a Wegner estimate which
implies Hoelder continuity of the integrated density of states