Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric exclusion processes

• 成果类型: Article
• 署名作者: Seppäläinen, T; Sethuraman, S
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; Iowa State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 148-169
• 关键词: CENTRAL-LIMIT-THEOREM; tagged particle; fluctuations; equilibrium

摘要

Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with nonzero drift. Let the process be stationary with product Bernoulli invariant distribution at density rho. Place a second-class particle initially at the origin. For the case rho not equal 1/2 we show that the time spent by the second-class particle at the origin has finite expectation. This strong transience is then used to prove that variances of additive functionals of local mean-zero functions are diffusive when rho not equal 1/2. As a corollary to previous work, we deduce the invariance principle for these functionals. The main arguments are comparisons of H-1 norms, a large deviation estimate for second-class particles and a relation between occupation times of second-class particles, and additive functional variances.