  For stationary KPZ growth in 1+1 dimensions the height fluctuations are
governed by the Baik-Rains distribution. Using the totally asymmetric single
step growth model, alias TASEP, we investigate height fluctuations for a
general class of spatially homogeneous random initial conditions. We prove that
for TASEP there is a one-parameter family of limit distributions, labeled by
the diffusion coefficient of the initial conditions. The distributions are
defined through a variational formula. We use Monte Carlo simulations to obtain
their numerical plots. Also discussed is the connection to the six-vertex model
at its conical point.
