Seminars & Colloquia Calendar

Abstract:  I will discuss random lattice configurations in two dimensions whose probability distribution follows some version of a Gibbs property. Examples include random (lozenge or domino) tilings and square ice (six vertex) model. Gibbs measures with fixed boundary conditions often display arctic curve phenomena, i.e., a coexistence of different phases. I will outline several results on the local behavior of random configurations in the bulk of a phase or at an interface between phases, and on global asymptotics leading to the Gaussian Free Field. I will also describe certain new Markov dynamics preserving the class of Gibbs measures which adds an extra dimension to the picture.