LIMIT DISTRIBUTIONS FOR KPZ GROWTH MODELS WITH SPATIALLY HOMOGENEOUS RANDOM INITIAL CONDITIONS

• Published in: The Annals of applied probability Vol. 28; no. 3; pp. 1573 - 1603
• Main Authors: Chhita, S., Ferrari, P. L., Spohn, H.
• Format: Journal Article
• Language: English
• Published: Hayward Institute of Mathematical Statistics 01-06-2018
• Subjects: Computer simulation; Diffusion coefficient; Initial conditions; Mathematical models; Monte Carlo simulation; Partial differential equations; Random variables; Skewed distributions; Stochastic models; Variations
• ISSN: 1050-5164; 2168-8737
• DOI: 10.1214/17-AAP1338

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.