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Abstract: We review a geometric approach to proving absolutely continuous ac spectrumfor random and deterministic Schr\-odinger operators developed in\cite{FHS1,FHS2,FHS3,FHS4}. We study decaying potentials in one dimension andpresent a simplified proof of ac spectrum of the Anderson model on trees. Thelatter implies ac spectrum for a percolation model on trees. Finally, weintroduce certain loop tree models which lead to some interesting openproblems.



Author: Richard Froese, David Hasler, Wolfgang Spitzer

Source: https://arxiv.org/







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