The Magnetic Laplacian Acting on Discrete Cusps

We introduce the notion of discrete cusp for a weighted graph. In this context, we prove that the form-domain of the magnetic Laplacian and that of the non-magnetic Laplacian can be different. We establish the emptiness of the essential spectrum and compute the asymptotic of eigenvalues for the magnetic Laplacian.

2010 Mathematics Subject Classification: 34L20, 47A10, 05C63, 47B25, 47A63, 81Q10

Keywords and Phrases: discrete magnetic Laplacian, locally finite graphs, eigenvalues, asymptotic, form-domain

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