**
**

**Dietlein, Adrian; Gebert, Martin; Hislop, Peter D.; Klein, Abel and 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 R-d. In: International Mathematics Research Notices, No. 21: pp. 6673-6697**

**Full text not available from 'Open Access LMU'.**

## Abstract

We obtain a bound on the expectation of the spectral shift function (SSF) for alloy-type random Schrodinger operators on R-d 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 Schrodinger 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 Schrodinger operators.

Item Type: | Journal article |
---|---|

Faculties: | Mathematics, Computer Science and Statistics > Mathematics |

Subjects: | 500 Science > 510 Mathematics |

ISSN: | 1073-7928 |

Language: | English |

Item ID: | 66379 |

Date Deposited: | 19. Jul 2019, 12:19 |

Last Modified: | 04. Nov 2020, 13:47 |