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.
Correlations of the characteristic polynomials in the Gaussian Unitary Ensemble or a singular Hankel determinant
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abstract
We obtain large n asymptotics for products of powers of the absolute values of the characteristic polynomials in the Gaussian Unitary Ensemble of n\times n matrices. Our results can also be interpreted as asymptotics of the determinant of a Hankel matrix whose symbol is supported on the real line and possesses power-like (Fisher-Hartwig) singularities.
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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.