1209.1001 (Yves Colin De Verdière et al.)

Scattering theory for graphs isomorphic to a homogeneous tree at
infinity    [PDF]

Yves Colin De Verdière, Francoise Truc

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.

View original: http://arxiv.org/abs/1209.1001