Eigenvalues of Toeplitz matrices in the bulk of the spectrum

Abstract

The authors analyze the asymptotics of eigenvalues of Toeplitz matrices with certain continuous and discontinuous symbols. In particular, the authors prove a conjecture of Levitin and Shargorodsky on the near-periodicity of Toeplitz eigenvalues.

arXiv comment17 pages, small changes, title modified

Cited by in corpus (8)

• Toeplitz determinants with merging singularities
• Eigenvalues of even very nice Toeplitz matrices can be unexpectedly erratic
• A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants
• Eigenvalues of tridiagonal Hermitian Toeplitz matrices with perturbations in the off-diagonal corners
• Cyclic Pólya Ensembles on the Unitary Matrices and their Spectral Statistics
• Asymptotics of the eigenvalues of seven-diagonal Toeplitz matrices of a special form
• On the Asymptotic Equivalence of Circulant and Toeplitz Matrices
• Riemann-Hilbert Characterisation of Rational Functions with a General Distribution of Poles on the Extended Real Line Orthogonal with Respect to Varying Exponential Weights: Multi-Point Padé Approximants and Asymptotics