Random matrix asymptotics for the six-vertex model.

Vadim Gorin (MIT)

Abstract :

The six-vertex (or "square-ice") model is one of the most well-studied examples of exactly-solvable lattice models of statistical mechanics. The developments of the last 15 years suggest that the asymptotic behavior of this model should be governed by the probability distributions of random matrix origin. However, until recently the rigorous mathematical results in this direction were restricted to the so-called free fermion case, when the model can be analyzed via determinantal point processes. In my talk we will discuss two results outside the free fermions, and see how the random matrix distributions, namely the Gaussian Unitary Ensemble and the Tracy-Widom distribution F_2, emerge.