Consider the two-dimensional lattice Z^2 as a graph, where edges connect neighbouring vertices. A six-vertex configuration is an orientation of the edges satisfying the ice rule: at each vertex, exactly two edges point in and two point out. This terminology originates from the interpretation of the six-vertex model as a statistical model of ice formation.

In this talk, we will study random six-vertex configurations sampled from a natural probability distribution. The main result of this work is a new determinantal formula for correlation functions of the model. The proof relies on a bijection between six-vertex configurations and ensembles of non-intersecting lattice paths, which allows the correlations to be expressed in terms of determinants.

This is joint work with Samuel G. G. Johnston.