A Sears-type self-adjointness result for discrete magnetic Schrِdinger operators

In the context of a weighted graph with vertex set V and bounded vertex degree, we give a sufficient condition for the essential self-adjointness of the operator Δ σ + W , where Δ σ is the magnetic Laplacian and W : V → R is a function satisfying W ( x ) ≥ − q ( x ) for all x ∈ V , with q : V → [ 1 , ∞ ) . The condition is expressed in terms of completeness of a metric that depends on q and the weights of the graph. The main result is a discrete analogue of the results of I. Oleinik and M.A. Shubin in the setting of non-compact Riemannian manifolds.