On the asymptotic distribution of eigenvalues of banded matrices
This paper concerns the density of states for unbounded banded Hermitian matrices J with any band width and possibly variable off-diagonal elements, as they occur in some physical models. Two widely used definitions of a density-of-state measure (one based on taking functions of a truncate of J, and the other on truncating functions of J) are shown to be equivalent also in the unbounded case. Then the author discusses the variance of density of states under unbounded perturbations and the extension of those definitions to J's with unbounded essential spectrum, based on the known method of renormalizing the truncates of J so as to make them essentially bounded. Several examples are given.
scientific article; zbMATH DE number 4053808
scientific article