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Some new estimates on the spectral shift function associated with random Schrödinger operators (2006)
| Content Provider | CiteSeerX |
|---|---|
| Author | Hislop, Peter D. Klopp, Frederic Combes, Jean-Michel |
| Abstract | We prove some new pointwise-in-energy bounds on the expectations of various spectral shift functions (SSF) associated with random Schrödinger 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 Schrödinger operators [5]. For lattice models, we also obtain a representation of the infinite-volume density of states in terms of the expectation of a SSF for a single-site perturbation. For continuum models, the corresponding measure, whose density is given by this SSF, is absolutely continuous with respect to the density of states and agrees with it in certain cases. As an application of one-parameter spectral averaging, we give a short proof of the classical pointwise upper bound on the SSF for finite-rank perturbations. |
| File Format | |
| Publisher Date | 2006-01-01 |
| Access Restriction | Open |
| Subject Keyword | Single-site Perturbation Finite-rank Perturbation Anderson-type Random Potential New Pointwise-in-energy Bound New Wegner Estimate Certain Case Spectral Shift Function Corresponding Measure Various Spectral Shift Function Random Schr Dinger Operator Short Proof Institut Universitaire Infinite-volume Density Lattice Model Finite-volume Random Schr Dinger Operator Continuum Model New Estimate One-parameter Spectral Averaging Classical Pointwise Upper Bound |
| Content Type | Text |
