BUSEMANN FUNCTIONS AND THE SPEED OF A SECOND CLASS PARTICLE IN THE RAREFACTION FAN

• 成果类型: Article
• 署名作者: Cator, Eric; Pimentel, Leandro P. R.
• 署名单位: Delft University of Technology; Universidade Federal do Rio de Janeiro
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP709
• 发表日期: 2013
• 页码: 2401-2425
• 关键词: behavior

摘要

In this paper we will show how the results found in [Probab. Theory Related Fields 154 (2012) 89-125], about the Busemann functions in last-passage percolation, can be used to calculate the asymptotic distribution of the speed of a single second class particle starting from an arbitrary deterministic configuration which has a rarefaction fan, in either the totally asymetric exclusion process or the Hammersley interacting particle process. The method will be to use the well-known last-passage percolation description of the exclusion process and of the Hammersley process, and then the well-known connection between second class particles and competition interfaces.