Abstract
We review a geometric approach to proving absolutely continuous (ac) spectrum for random and deterministic Schrödinger operators developed in [9–12]. 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.
Mathematics Subject Classification (2000). 82B44.
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Froese, R., Hasler, D., Spitzer, W. (2011). A Geometric Approach to Absolutely Continuous Spectrum for Discrete Schrödinger Operators. In: Lenz, D., Sobieczky, F., Woess, W. (eds) Random Walks, Boundaries and Spectra. Progress in Probability, vol 64. Springer, Basel. https://doi.org/10.1007/978-3-0346-0244-0_11
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DOI: https://doi.org/10.1007/978-3-0346-0244-0_11
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