Limit distributions for KPZ growth models with spatially homogeneous random initial conditions

Understand

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.