In this paper we present a class of Anderson type operators with independent, non-stationary (non-decaying) random potentials supported on a subset of positive density in the odd-dimensional lattice and prove the existence of pure absolutely continuous spectrum in the middle of the band for small disorder.
Localization for random operators on $\mathbb{Z}^d$ with the long-range hopping
On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials
Multiscale Analysis and Localization of Random Operators
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