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.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00283404
Contributor : Jean Michel Maillet <>
Submitted on : Tuesday, July 29, 2008 - 12:53:24 AM
Last modification on : Tuesday, April 23, 2019 - 10:28:11 AM
Long-term archiving on : Tuesday, September 21, 2010 - 5:27:00 PM

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N. Kitanine, Karol Kozlowski, Jean Michel Maillet, N. A. Slavnov, Véronique Terras. Riemann-Hilbert approach to a generalized sine kernel and applications. Communications in Mathematical Physics, Springer Verlag, 2009, 291 (3), pp.691-761. ⟨10.1007/s00220-009-0878-1⟩. ⟨ensl-00283404v2⟩

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