Spectral analysis for adjacency operators on graphs

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.

16 pages, 9 figures

References in corpus (2)

• Spectral Analysis of Percolation Hamiltonians
• Toeplitz algebras and spectral results for the one-dimensional Heisenberg model

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