Some new estimates on the spectral shift function associated with random Schrödinger operators

Details Some new estimates on the spectral shift function associated with random Schrödinger operators Some new estimates on the spectral shift function associated with random Schrödinger operators

2006-05-09

arxiv.org/abs/math-ph/0605030v2

Physics

Mathematical Physics

Some results were improved and some proofs simplified

Scientific paper

We prove some new pointwise-in-energy bounds on the expectations of various spectral shift functions associated with random Schr\"{o}dinger operators in the continuum having Anderson-type random potentials in both finite-volume and infinite-volume. These estimates are a consequence of our new Wegner estimate for finite-volume random Schr\"{o}dinger operators. For lattice models, we also obtain a representation of the infinite-volume density of states in terms of a spectral shift function. For continuum models, the corresponding measure is absolutely continuous with respect to the density of states and agrees with it in certain cases. We present a variant of a new spectral averaging result and use it to prove a pointwise upper bound on the SSF for finite-rank perturbations.

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