Patterns in the Kardar-Parisi-Zhang equation

Abstract

We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a network of localized growth modes. Scaling in 1d is associated with a gapless domain wall mode. The method also provides an independent argument for the existence of an upper critical dimension.