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Full-Text Articles in Physical Sciences and Mathematics
Toeplitz Determinants With Perturbations In The Corners, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Toeplitz Determinants With Perturbations In The Corners, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Pomona Faculty Publications and Research
This paper is devoted to exact and asymptotic formulas for the determinants of Toeplitz matrices with perturbations by blocks of fixed size in the four corners. If the norms of the inverses of the unperturbed matrices remain bounded as the matrix dimension goes to infinity, then standard perturbation theory yields asymptotic expressions for the perturbed determinants. This premise is not satisfied for matrices generated by so-called Fisher-Hartwig symbols. In that case we establish formulas for pure single Fisher-Hartwig singularities and for the Hermitian matrices induced by general Fisher-Hartwig symbols.