Abstract
This paper explores the relationship between the spectra of perturbed infinite banded Laurent matricesL(a)+K and their approximations by perturbed circulant matricesC n (a)+P n KP n for largen. The entriesK jk of the perturbation matrices assume values in prescribed sets Ω jk at the sites (j, k) of a fixed finite setE, and are zero at the sites (j, k) outsideE. WithK EΩ denoting the ensemble of these perturbation matrices, it is shown that
under several fairly general assumptions onE and Ω.
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Böttcher, A., Embree, M. & Lindner, M. Spectral approximation of banded Laurent matrices with localized random perturbations. Integr equ oper theory 42, 142–165 (2002). https://doi.org/10.1007/BF01275512
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DOI: https://doi.org/10.1007/BF01275512