Probability and Stochastic Analysis - University of Bonn

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

with Sunil Chhita and Herbert Spohn.

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 roughness 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 is conical point.

Postscript file: [PS]

PDF file: [PDF]

arXiv: 1611.06690