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Existence of the density of states for one-dimensional alloy-type potentials with small support

Werner Kirsch·Ivan Veselic'
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Abstract

We study spectral properties of Schrödinger operators with random potentials of alloy type on $L^2(\RR)$ and their restrictions to finite intervals. A Wegner estimate for non-negative single site potentials with small support is proven. It implies the existence and local uniform boundedness of the density of states. Our estimate is valid for all bounded energy intervals. Wegner estimates play a key role in an existence proof of pure point spectrum.

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Werner Kirsch, Ivan Veselic'. 2002-04-15. Existence of the density of states for one-dimensional alloy-type potentials with small support. https://arxiv.org/abs/math-ph/0204030

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