Absolutely continuous spectrum for random operators on trees of finite cone type

Autoren: Matthias Keller, Daniel Lenz, Simone Warzel (2012)

We study the spectrum of random operators on a large class of trees. These trees have finitely many cone types and they can be constructed by a substitution rule. The random operators are perturbations of Laplace type operators either by random potentials or by random hopping terms, i.e., perturbations of the off-diagonal elements. We prove stability of arbitrary large parts of the absolutely continuous spectrum for sufficiently small but extensive disorder.

Journal d'Analyse Mathematique

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