Limit distributions for KPZ growth models with spatially homogeneous   random initial conditions
  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. 
S. Chhita (1), P.L. Ferrari (2), and H. Spohn (3) ((1) Durham   University, (2) Bonn University, (3) Technical University of...
math.PR math-ph math.MP