Boundary statistics for the six‐vertex model with DWBC

We study the behavior of configurations in the symmetric six‐vertex model with weights in the square with Domain Wall Boundary Conditions as . We prove that when , configurations near the boundary have fluctuations of order and are asymptotically described by the GUE‐corners process of random matrix theory. On the other hand, when , the fluctuations are of finite order and configurations are asymptotically described by the stochastic six‐vertex model in a quadrant. In the special case (which implies ), the limit is expressed as the ‐exchangeable random permutation of infinitely many letters, distributed according to the infinite Mallows measure.