Riemann-Hilbert approach to a generalized sine kernel and applications
Mathematical Physics
2011-10-07 v3 math.MP
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.
Keywords
Cite
@article{arxiv.0805.4586,
title = {Riemann-Hilbert approach to a generalized sine kernel and applications},
author = {N. Kitanine and Karol K. Kozlowski and Jean Michel Maillet and N. A. Slavnov and Véronique Terras},
journal= {arXiv preprint arXiv:0805.4586},
year = {2011}
}
Comments
74 pages