M. Mantoiu, S. Richard, R. Tiedra de Aldecoa
Spectral analysis for adjacency operators on graphs
(375K, postscript)
ABSTRACT. We put into evidence graphs with adjacency operator whose singular subspace is prescribed by
the kernel of an auxiliary operator. In particular, for a family of graphs called admissible,
the singular continuous spectrum is absent and there is at most an eigenvalue located at the
origin. Among other examples, the one-dimensional XY model of solid-state physics is
covered. The proofs rely on commutators methods.