On Determinants of Integrable Operators with Shifts

In the talk, some recent results of the asymptotic analysis of the Fredholm determinants of integral operators appearing in the study of the correlation functions in non-free fermion exactly solvable quantum field models will be presented. Specially, we shall consider the shifted sine-kernel as a case study. The talk is based on the earlier works of the speaker with V. Korepin, A. Izergin, N. Slavnov and K. Koslowski and on the ongoing project with T. Bothner, A. Simon and K. Kozlowski.