JournalsdmVol. 22pp. 1709–1727

The Magnetic Laplacian Acting on Discrete Cusps

  • Sylvain Golénia

    Univ. Bordeaux, Bordeaux INP, CNRS, IMB, UMR 5251, F-33400 Talence, France

  • Françoise Truc

    Grenoble University, Institut Fourier, Unité mixte de recherche, CNRS-UJF, 5582 BP 74, 38402-Saint Martin d'Hères Cedex, France
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Abstract

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.

Cite this article

Sylvain Golénia, Françoise Truc, The Magnetic Laplacian Acting on Discrete Cusps. Doc. Math. 22 (2017), pp. 1709–1727

DOI 10.4171/DM/608