Probability and Stochastic Analysis - University of Bonn

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

with Alexei Borodin and Ivan Corwin.

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.

Postscript file: [PS]

PDF file: [PDF]

arXiv: 1612.00321