  A special class of four-point correlation functions in the maximally
supersymmetric Yang-Mills theory is given by the square of the Fredholm
determinant of a generalized Bessel kernel. In this note, we re-express its
logarithmic derivatives in terms of a two-dimensional Riemann-Hilbert problem.
We solve the latter in the null limit making use of the Deift-Zhou steepest
descent. We reproduce the exact octagonal anomalous dimension in 't Hooft
coupling and provide its novel formulation as a convolution of the non-linear
quasiclassical phase with the Fermi distribution in the limit of the infinite
chemical potential.
