Riemann-Hilbert approach to a generalized sine kernel and applications

N. Kitanine 1 Karol Kozlowski 2 Jean Michel Maillet 2 N. A. Slavnov 3 Véronique Terras 2, 4
1 LPTM - Laboratoire de Physique Théorique et Modélisation
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
3 SMI - Steklov Mathematical Institute
4 LPTA - Laboratoire de Physique Théorique et Astroparticules
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.
keyword : Fredholm determinant Generalized sine kernel Wiener-Hopf operators Integrable models
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00283404
Contributor : Jean Michel Maillet <>
Submitted on : Wednesday, October 5, 2011 - 9:47:14 AM
Last modification on : Wednesday, November 20, 2019 - 3:27:15 AM
Long-term archiving on : Friday, January 6, 2012 - 2:21:32 AM

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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-00283404v3⟩

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