A 4x4 Riemann-Hilbert formalism gives large-n asymptotics for Toeplitz+Hankel determinants with independent symbols, conditional on a non-degeneracy bound and verified for an explicit family.
Eigenvalues of Toeplitz matrices in the bulk of the spectrum
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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.
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A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants
A 4x4 Riemann-Hilbert formalism gives large-n asymptotics for Toeplitz+Hankel determinants with independent symbols, conditional on a non-degeneracy bound and verified for an explicit family.