Geodesic
The Magnetic Laplacian Acting on Discrete Cusps
Documenta mathematica, Tome 22 (2017), pp. 1709-1727
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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.
DOI : 10.4171/dm/608
Classification : 05C63, 34L20, 47A10, 47A63, 47B25, 81Q10
Mots-clés : eigenvalues, discrete magnetic Laplacian, locally finite graphs, asymptotic, form-domain 
@article{10_4171_dm_608,
     author = {Sylvain Gol\'enia and Fran\c{c}oise Truc},
     title = {The {Magnetic} {Laplacian} {Acting} on {Discrete} {Cusps}},
     journal = {Documenta mathematica},
     pages = {1709--1727},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/608},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/608/}
}
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Sylvain Golénia; Françoise Truc. The Magnetic Laplacian Acting on Discrete Cusps. Documenta mathematica, Tome 22 (2017), pp. 1709-1727. doi: 10.4171/dm/608

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