The magnetic Laplacian acting on discrete cusps

Published 9 Jul 2015 in math.SP, math-ph, math.FA, and math.MP | (1507.02638v3)

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

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