A geometric approach to absolutely continuous spectrum for discrete Schrödinger operators
arXiv:1004.4843
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.
Review, Alp workshop "Spectral and probabilistic properties of random walks on random graphs", St. Kathrein (2009).