Maurice Duits (KTH, Stockholm)

The Gaussian free field and anisotropic growth

We start by introducing the Gaussian free field in the context of fluctuations of random surfaces that arise in random matrix theory. We then discuss a stochastic evolution on a system of interlacing particles on the square lattice, that falls in the anisotropic KPZ class. For large time, a deterministic shape appears that describes the limiting distribution of the particles. We will focus on the global fluctuations around this limit shape. As we shall see, even in situations where the limit shape is no longer smooth, these fluctuations are typically characterized by the Gaussian free field.