We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance-dependent correlation functions of integrable models described by a six-vertex $R$-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann–Hilbert based analysis.
"Riemann–Hilbert approach to the time-dependent generalized sine kernel." Adv. Theor. Math. Phys. 15 (6) 1655 - 1743, December 2011.