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Journal Articles Communications in Mathematical Physics Year : 2009

Riemann-Hilbert approach to a generalized sine kernel and applications

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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.
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Dates and versions

ensl-00283404 , version 1 (29-05-2008)
ensl-00283404 , version 2 (29-07-2008)
ensl-00283404 , version 3 (05-10-2011)

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Cite

N. Kitanine, Karol K. Kozlowski, Jean Michel Maillet, N. A. Slavnov, Véronique Terras. Riemann-Hilbert approach to a generalized sine kernel and applications. Communications in Mathematical Physics, 2009, 291 (3), pp.691-761. ⟨10.1007/s00220-009-0878-1⟩. ⟨ensl-00283404v3⟩
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