Riemann-Hilbert approach to a generalized sine kernel and applications

Details Riemann-Hilbert approach to a generalized sine kernel and applications Riemann-Hilbert approach to a generalized sine kernel and applications

2008-05-29

arxiv.org/abs/0805.4586v3

Communications in Mathematical Physics 3, 291 (2009) 691-761

Physics

Mathematical Physics

74 pages

Scientific paper

10.1007/s00220-009-0878-1

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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