Boundary statistics for the six‐vertex model with DWBC

Abstract

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.