The Kardar-Parisi-Zhang (KPZ) equation describes the stochastic evolution of a growing surface. In one dimension, exact scaling functions for the fluctuations of the height of the interface around its mean value have been obtained. These scaling functions have been derived first from microscopic realizations of the KPZ equation such as the asymmetric simple exclusion process and the polynuclear growth model. More recently, it has been possible to obtain some of these scaling functions directly from the Cole-Hopf solution of the KPZ equation using the replica method.

T.U. Munich