The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials.

We consider Schrödinger operators in ℓ 2 (Z) whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the ergodic term is generated by a homeomorphism of a connected compact metric space and a continuous sampling function, we show that the almost sure spectrum arises in an explicitly described way from the unperturbed spectrum and the topological support of the single-site distribution. In particular, assuming that the latter is compact and contains at least two points, this explicit description of the almost sure spectrum shows that it will always be given by a finite union of non-degenerate compact intervals. The result can be viewed as a far reaching generalization of the well known formula for the spectrum of the classical Anderson model. [ABSTRACT FROM AUTHOR]

Copyright of Geometric & Functional Analysis is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)