Essential self-adjointness for combinatorial Schrödinger operators. III: Magnetic fields
In this article, the authors prove the essential self-adjointness of the discrete magnetic Laplacian acting on an infinite graph of bounded degree. They give a justification to the fact that if \((c, |B|)\) tends to infinity then the operator is essentially self-adjoint. Here \(c\) encodes the information related to the weights and \(|B|\) the strength of the magnetic field. The first step is to prove a lower bound for the quadratic form associated to the operator thanks to an effective potential. This is the main novelty. The second step is to use an Agmon estimate; the authors refer to their previous work for the related proofs. In the last section, the authors propose some open questions. For Parts I and II, see \textit{N. Torki-Hamza} [Confluentes Math. 2, No.~3, 333--350 (2010; Zbl 1203.05109)] and \textit{Y. Colin de Verdière}, \textit{N. Torki-Hamza} and \textit{F. Truc} [Math. Phys. Anal. Geom. 14, No.~1, 21--38 (2011; Zbl 1244.05155)], respectively.
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