Anisotropic growth of random surfaces in 2+1 dimensions

Understand

We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class.

• Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models.
• We show that correlation functions associated to our models have determinantal structure, and we study large time asymptotics for one of the models.
• The main asymptotic results are: (1) The growing surface has a limit shape that consists of facets interpolated by a curved piece.