Discrete alloy-type models: Regularity of distributions and recent results

Abstract

We consider discrete random Schrödinger operators on ${\ell }^2({\mathbb{Z}}^d)$ with a potential of discrete alloy-type structure. That is, the potential at lattice site $x\in {\mathbb{Z}}^d$ 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 $\tau$-Hölder 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.

20 pages, 0 figures

References in corpus (1)

• An Invitation to Random Schroedinger operators

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