Its, Alexander R.Kozlowski, K. K.2016-12-092016-12-092016Its, A. R., & Kozlowski, K. K. (2016). Large-x Analysis of an Operator-Valued Riemann–Hilbert Problem. International Mathematics Research Notices, 2016(6), 1776-1806.https://hdl.handle.net/1805/11593The purpose of this paper is to push forward the theory of operator-valued Riemann–Hilbert problems and demonstrate their effectiveness in respect to the implementation of a non-linear steepest descent method á la Deift–Zhou. In this paper, we demonstrate that the operator-valued Riemann–Hilbert problem arising in the characterization of so-called cc-shifted integrable integral operators allows one to extract the large-xx asymptotics of the Fredholm determinant associated with such operators.enPublisher PolicyRiemann Hilbert problemsFredholm determinantArticle