Scattering theory for graphs isomorphic to a homogeneous tree at infinity

Yves Colin de Verdière (1) , Francoise Truc (1)

1 IF - Institut Fourier

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.

Mots clés: scattering on graphs; spectral measure; homogeneous tree; eigenfunction expansion

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Combinatoire [math.CO]

Yves Colin de Verdière, Francoise Truc. Scattering theory for graphs isomorphic to a homogeneous tree at infinity. 2013. ⟨hal-00728357v2⟩