Norbert Peyerimhoff, Martin Tautenhahn, Ivan Veselić : Wegner estimate for alloy-type models with sign-changing exponentially decaying single-site potentials

Author(s):

Norbert Peyerimhoff
Martin Tautenhahn
Ivan Veselić

Title:

Wegner estimate for alloy-type models with sign-changing exponentially decaying single-site potentials

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 09, 2011

Mathematics Subject Classification:

82B44	[]
60H25	[]
35J10	[]

Abstract:

We study Schrödinger operators on $L2 (\RR^d)$ and $\ell2(\ZZ^d)$ with a random potential of alloy-type. The single-site potential is assumed to be exponentially decaying. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. In the described situation a Wegner estimate which is polynomial in the volume of the box and linear in the size of the energy interval holds. It is applicable as an ingredient for a localisation proof via multiscale analysis.

Keywords:

random Schrödinger operators, alloy-type model, discrete alloy-type model, integrated density of states, Wegner estimate, single-site potential

Language:

English

Publication time:

06/2011