Localization via fractional moments for models on $\mathbb{Z}$ with single-site potentials of finite support

Abstract

One of the fundamental results in the theory of localization for discrete Schrödinger operators with random potentials is the exponential decay of Green's function and the absence of continuous spectrum. In this paper we provide a new variant of these results for one-dimensional alloy-type potentials with finitely supported sign-changing single-site potentials using the fractional moment method.

LaTeX-file, 26 pages with 2 LaTeX figures

References in corpus (6)

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• Correlations Estimates in the Lattice Anderson Model
• Spectral extrema and Lifshitz tails for non monotonous alloy type models
• Wegner estimate and the density of states of some indefinite alloy type Schroedinger Operators
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Cited by in corpus (7)

• Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method
• Minami's estimate: beyond rank one perturbation and monotonicity
• Low lying eigenvalues of randomly curved quantum waveguides
• Low lying spectrum of weak-disorder quantum waveguides
• Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials
• Level Spacing for Non-Monotone Anderson Models
• Quantum Hamiltonians with weak random abstract perturbation. II. Localization in the expanded spectrum