(2+1)-dimensional growth models and the AKPZ universality class, talk 1

Abstract: I will discuss 2+1-dimensional growth models and in particular the so-called Anisotropic KPZ (AKPZ) universality class. This comprises models that have the same growth and roughness exponents as the two-dimensional stochastic heat equation with additive noise (2d-SHE). I will review recent rigorous results both on discrete growth models in this class, and on the AKPZ equation itself. The latter is an anisotropic variant of the two-dimensional KPZ stochastic PDE (with noise regularization). In the physics literature, the AKPZ equation was conjectured to have the same scaling limit as the 2d-SHE, but we will show that this is not entirely true. Indeed, while the 2d-SHE is invariant under diffusive rescaling, this does not hold (not even asymptotically on large scales) for the AKPZ equation, and logarithmic corrections to the scaling are needed instead. [The last part is based on joint work with G. Cannizzaro and D. Erhard]