Riemann-Hilbert approach to a generalized sine kernel and applications

Abstract

We investigate the asymptotic behavior of a generalized sine kernel acting on a finite size interval [-q,q]. We determine its asymptotic resolvent as well as the first terms in the asymptotic expansion of its Fredholm determinant. Further, we apply our results to build the resolvent of truncated Wiener--Hopf operators generated by holomorphic symbols. Finally, the leading asymptotics of the Fredholm determinant allows us to establish the asymptotic estimates of certain oscillatory multidimensional coupled integrals that appear in the study of correlation functions of quantum integrable models.

74 pages

References in corpus (4)

• Temperature Correlation of Quantum Spins
• Gap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on an arc of the unit circle
• Toeplitz and Hankel determinants with singularities: announcement of results
• Truncated Wiener-Hopf operators with Fisher Hartwig singularities

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