Six-vertex Models and the GUE-corners Process

Abstract

Abstract We consider a class of probability distributions on the six-vertex model, which originates from the higher spin vertex models of [13]. We define operators, inspired by the Macdonald difference operators, which extract various correlation functions, measuring the probability of observing different arrow configurations. For the class of models we consider, the correlation functions can be expressed in terms of multiple contour integrals, which are suitable for asymptotic analysis. For a particular choice of parameters we analyze the limit of the correlation functions through the steepest descent method. Combining this asymptotic statement with some new results about Gibbs measures on Gelfand–Tsetlin cones and patterns, we show that the asymptotic behavior of our six-vertex model near the boundary is described by the Gaussian Unitary Ensemble-corners process.