Competition interfaces and second class particles

• 成果类型: Article
• 署名作者: Ferrari, PA; Pimentel, LPR
• 署名单位: Universidade de Sao Paulo
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000080
• 发表日期: 2005
• 页码: 1235-1254
• 关键词: asymmetric simple exclusion; first-passage percolation; geodesics; density; profile; limit

摘要

The one-dimensional nearest-neighbor totally asymmetric simple exclusion process can be constructed in the same space as a last-passage percolation model in Z(2). We show that the trajectory of a second class particle in the exclusion process can be linearly mapped into the competition interface between two growing clusters in the last-passage percolation model. Using technology built up for geodesics in percolation, we show that the competition interface converges almost surely to an asymptotic random direction. As a consequence we get a new proof for the strong law of large numbers for the second class particle in the rarefaction fan and describe the distribution of the asymptotic angle of the competition interface.