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

Chhita, Sunil; Ferrari, Patrik L.; Spohn, Herbert

Abstract

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.

Citation

Chhita, S., Ferrari, P. L., & Spohn, H. (2018). Limit distributions for KPZ growth models with spatially homogeneous random initial conditions. Annals of Applied Probability, 28(3), 1573-1603. https://doi.org/10.1214/17-aap1338

• Journal Article Type: Article
• Acceptance Date: Aug 10, 2017
• Online Publication Date: Jun 1, 2018
• Publication Date: Jun 1, 2018
• Deposit Date: Sep 21, 2017
• Publicly Available Date: Sep 25, 2017
• Journal: Annals of Applied Probability
• Print ISSN: 1050-5164
• Publisher: Institute of Mathematical Statistics
• Peer Reviewed: Peer Reviewed
• Volume: 28
• Issue: 3
• Pages: 1573-1603
• DOI: https://doi.org/10.1214/17-aap1338
• Related Public URLs: https://arxiv.org/abs/1611.06690