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

Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes