Scattering theory for graphs isomorphic to a homogeneous tree at infinity

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 Schrödinger operators in Euclidian spaces.

This paper will appear in Journal of Mathematical Physics