Anomalous shock fluctuations in TASEP and last passage percolation models

• 成果类型: Article
• 署名作者: Ferrari, Patrik L.; Nejjar, Peter
• 署名单位: University of Bonn
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0544-6
• 发表日期: 2015
• 页码: 61-109
• 关键词: simple exclusion process; polynuclear growth; airy(2) processes; distributions; limit

摘要

We consider the totally asymmetric simple exclusion process with initial conditions and/or jump rates such that shocks are generated. If the initial condition is deterministic, then the shock at time will have a width of order . We determine the law of particle positions in the large time limit around the shock in a few models. In particular, we cover the case where at both sides of the shock the process of the particle positions is asymptotically described by the Airy process. The limiting distribution is a product of two distribution functions, which is a consequence of the fact that at the shock two characteristics merge and of the slow decorrelation along the characteristics. We show that the result generalizes to generic last passage percolation models.