The transition between order to disorder in the Seppäläinen-Johansson model

We study the Seppäläinen-Johansson model of first-passage percolation along a region of the plane where it moves from an ordered to a disordered phase, represented by a 2nd order discontinuity in its limit shape function. The fluctuations in this transition region are of order one, and we determine that certain limiting statistics are described by Fredholm determinants and are closely related to the largest eigenvalue of the GUE.