Asymptotics of eigenvalues of large symmetric Toeplitz matrices with smooth simple-loop symbols

2019/03/25 by A.A. Batalshchikov, Batalshchikov, A. A., Sergei M. Grudsky +9 · 1 citation
Mathematics · #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1903.10551

Abstract

This paper is devoted to the asymptotic behavior of all eigenvalues of Symmetric (in general non Hermitian) Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the complex plane line as the dimension of the matrices increases to infinity. The main result describes the asymptotic structure of all eigenvalues. The constructed expansion is uniform with respect to the number of eigenvalues. Keywords: Toeplitz matrices, eigenvalues, asymptotic expansions

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• Eigenvalues of the tetradiagonal Toeplitz matrices with diagonals 1, 0, 0, 1

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