Second class particles and cube root asymptotics for Hammersley's process

• 成果类型: Article
• 署名作者: Cator, Eric; Groeneboom, Piet
• 署名单位: Delft University of Technology; Vrije Universiteit Amsterdam
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000089
• 发表日期: 2006
• 页码: 1273-1295
• 关键词: growth-model; fluctuations

摘要

We show that, for a stationary version of Hammersley's process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly North-East path L(t, t) from (0, 0) to (t, t) is equal to 2E(t - X(t))+, where X(t) is the location of a second class particle at time t. This implies that both E(t - X(t))+ and the variance of L (t, t) are of order t(2/3). Proofs are based on the relation between the flux and the path of a second class particle, continuing the approach of Cator and Groeneboom