Domino tilings and the six-vertex model at its free-fermion point

At the free-fermion point, the six-vertex model with domain wall boundary conditions (DWBC) can be related to the Aztec diamond, a domino tiling problem. We study the mapping on the level of complete statistics for general domains and boundary conditions. This is obtained by associating with both models a set of non-intersecting lines in the Lindström–Gessel–Viennot (LGV) scheme. One of the consequences for DWBC is that the boundaries of the ordered phases are described by the Airy process in the thermodynamic limit.