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arXiv · 1004.4843

A geometric approach to absolutely continuous spectrum for discrete Schrödinger operators

Richard Froese·David Hasler·Wolfgang Spitzer
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Abstract

We review a geometric approach to proving absolutely continuous (ac) spectrum for random and deterministic Schrödinger operators developed in \cite{FHS1,FHS2,FHS3,FHS4}. We study decaying potentials in one dimension and present a simplified proof of ac spectrum of the Anderson model on trees. The latter implies ac spectrum for a percolation model on trees. Finally, we introduce certain loop tree models which lead to some interesting open problems.

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Richard Froese, David Hasler, Wolfgang Spitzer. 2010-04-27. A geometric approach to absolutely continuous spectrum for discrete Schrödinger operators. https://arxiv.org/abs/1004.4843

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