### Abstract

The motion of an interface separating a stable from an unstable phase is a well-studied problem in nonequilibrium dynamics, in particular since the field-theoretic formulation by Kardar, Parisi, and Zhang. For a one-dimensional interface many universal quantities of physical interest can be computed exactly. Surprisingly enough, there are links to the soft edge scaling of Gaussian unitary matrices. We explain the type of growth models which can be handled, how the connection to random matrices arises, and some of the predictions for one-dimensional growth.