The asymmetric exclusion process and random matrices

We consider the class of stochastic growth models in the Kardar-Parisi-Zhang
(KPZ) universality class. In 1+1 dimensions, for large growth time t, the
limit process describing the surface is the Airy_1 or the Airy_2 process,
depending on the curvature of the limit shape. The decay of the correlations
are however very different (superexponentially vs. polynomial). A second
aspect are the height-height correlations at different times. The space-time
turns out to be non-trivially fibred, with some space-time curves with slow
decorrelations.