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Scattering theory for graphs isomorphic to a homogeneous tree at infinity (1209.1001v2)
Published 5 Sep 2012 in math-ph, math.MP, and math.SP
Abstract: We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the adjacency operator on an homogeneous tree. We developp this scattering theory using the classical recipes for Schr\"odinger operators in Euclidian spaces.
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