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

Abstract 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 of covariances to those of 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. Keywords: 2+1 growth models, KPZ universality class, q-Whittaker processes, Gaussian Free Field, Space-time processGalileo Galilei Institute for Theoretical Physics (Arcetri, Italy)Kavli Institute for Theoretical PhysicsNational Science Foundation (U.S.) (Grant PHY-1125915)National Science Foundation (U.S.) (Grant DMS-1056390)National Science Foundation (U.S.) (Grant DMS-1607901)Simons Foundation. Postdoctoral FellowshipRadcliffe Institute for Advanced Study (Fellowship