Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes
  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. 
Alexei Borodin, Ivan Corwin, Patrik L. Ferrari
math.PR cond-mat.stat-mech math-ph math.MP