We obtain a bound on the expectation of the spectral shift function (SSF) for alloytype random Schrödinger 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 finite-volume Schrödinger operators in the region of localisation with a constant locally uniform in the energy. The application requires that the single-site 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 Schrödinger operators.
|Number of pages||25|
|Journal||International Mathematics Research Notices|
|State||Published - Nov 5 2018|
Bibliographical noteFunding Information:
This work was supported by the Deutsche Forschungsgemeinschaft [GE 2871/1-1 to M.G.]; partially supported by the National Science Foundation [DMS-1103104 to P.D.H.]; partially supported by the National Science Foundation [DMS-1001509 to A.K.].
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ASJC Scopus subject areas
- Mathematics (all)