A geometric approach to absolutely continuous spectrum for discrete Schr\"odinger operators
Mathematical Physics
2010-04-28 v1 Functional Analysis
math.MP
Abstract
We review a geometric approach to proving absolutely continuous (ac) spectrum for random and deterministic Schr\"odinger 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.
Keywords
Cite
@article{arxiv.1004.4843,
title = {A geometric approach to absolutely continuous spectrum for discrete Schr\"odinger operators},
author = {Richard Froese and David Hasler and Wolfgang Spitzer},
journal= {arXiv preprint arXiv:1004.4843},
year = {2010}
}
Comments
Review, Alp workshop "Spectral and probabilistic properties of random walks on random graphs", St. Kathrein (2009).