Communications in Mathematical Physics

, Volume 291, Issue 3, pp 691–761 | Cite as

Riemann–Hilbert Approach to a Generalised Sine Kernel and Applications

  • N. Kitanine
  • K. K. Kozlowski
  • J. M. Maillet
  • N. A. Slavnov
  • V. Terras
Article

Abstract

We investigate the asymptotic behaviour of a generalised 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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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • N. Kitanine
    • 1
  • K. K. Kozlowski
    • 2
  • J. M. Maillet
    • 2
  • N. A. Slavnov
    • 3
  • V. Terras
    • 2
  1. 1.LPTMUniversité de Cergy-Pontoise et CNRSCergy-PontoiseFrance
  2. 2.Laboratoire de PhysiqueENS Lyon et CNRSLyonFrance
  3. 3.Steklov Mathematical InstituteMoscowRussia

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