Dietlein, Adrian; Gebert, Martin; Hislop, Peter D.; Klein, Abel; Müller, Peter
(2018):
A Bound on the Averaged Spectral Shift Function and a Lower Bound on the Density of States for Random Schrodinger Operators on Rd.
In: International Mathematics Research Notices, No. 21: pp. 66736697

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Abstract
We obtain a bound on the expectation of the spectral shift function (SSF) for alloytype random Schrodinger operators on Rd in the region of localisation, corresponding to a change from Dirichlet to Neumann boundary conditions along the boundary of a finite volume. The bound scales with the area of the surface where the boundary conditions are changed. As an application of our bound on the SSF, we prove a reverse Wegner inequality for finitevolume Schrodinger operators in the region of localisation with a constant locally uniform in the energy. The application requires that the singlesite distribution of the independent and identically distributed random variables has a Lebesgue density that is also bounded away from zero. The reverse Wegner inequality implies a strictly positive, locally uniform lower bound on the density of states for these continuum random Schrodinger operators.