  We consider a discrete model for anisotropic (2+1)-dimensional growth of an
interface height function. Owing to a connection with q-Whittaker functions,
this system enjoys many explicit integral formulas. By considering certain
Gaussian stochastic differential equation limits of the model we are able to
prove a space-time limit to the (2+1)-dimensional additive stochastic heat
equation (or Edwards-Wilkinson equation) along characteristic directions. In
particular, the bulk height function converges to the Gaussian free field which
evolves according to this stochastic PDE.
