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.
Asymptotic formulas for determinants of a special class of Toeplitz + Hankel matrices
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abstract
We compute the asymptotics of the determinants of certain $n\times n$ Toeplitz + Hankel matrices $T_n(a)+H_n(b)$ as $n\to\infty$ with symbols of Fisher-Hartwig type. More specifically we consider the case where $a$ has zeros and poles and where $b$ is related to $a$ in specific ways. Previous results of Deift, Its and Krasovsky dealt with the case where $a$ is even. We are generalizing this in a mild way to certain non-even symbols.
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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.