Martin Tautenhahn, Ivan Veselić: Discrete alloy-type models: Regularity of distributions and recent results

Author(s):

Martin Tautenhahn
Ivan Veselić

Title:

Martin Tautenhahn, Ivan Veselić: Discrete alloy-type models: Regularity of distributions and recent results

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 05, 2014

Mathematics Subject Classification:

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

Abstract:

We consider discrete random Schr\"odinger operators on $\ell^2 (\ZZ^d)$ with a potential of discrete alloy-type structure. That is, the potential at lattice site $x \in \ZZ^d$ is given by a linear combination of independent identically distributed random variables, possibly with sign-changing coefficients. In a first part we show that the discrete alloy-type model is not uniformly $\tau$-H\"older continuous, a frequently used condition in the literature of Anderson-type models with general random potentials. In a second part we review recent results on regularity properties of spectral data and localization properties for the discrete alloy-type model.

Keywords:

Language:

English

Publication time:

03/2014