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.