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

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

2002-04-15

arxiv.org/abs/math-ph/0204030v1

Physics

Mathematical Physics

See also mp_arc, 02-144. In a different version to appear in the proceedings of the QMath-8 Conference, Taxco, Mexico, 2001

Scientific paper

We study spectral properties of Schr\"odinger 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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