  In this paper we consider a class of probability distributions on the
six-vertex model from statistical mechanics, which originate from the higher
spin vertex models of https://arxiv.org/abs/1601.05770. We define operators,
inspired by the Macdonald difference operators, which extract various
correlation functions, measuring the probability of observing different arrow
configurations. The development of our operators is largely based on the
properties of a remarkable family of symmetric rational functions, which were
previously studied in https://arxiv.org/abs/1410.0976.
  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 a 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 GUE-corners process.
