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

• 成果类型: Article
• 署名作者: Chhita, S.; Ferrari, P. L.; Spohn, H.
• 署名单位: Durham University; University of Bonn; Technical University of Munich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1338
• 发表日期: 2018
• 页码: 1573-1603
• 关键词: 6-vertex model; polynuclear growth; brownian-motion; fluctuations; tasep; UNIVERSALITY; percolation; covariance; TRANSITION; interfaces

摘要

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.