Central limit theorems for additive functionals of the simple exclusion process

• 成果类型: Article
• 署名作者: Sethuraman, S
• 署名单位: Iowa State University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 277-302
• 关键词: asymmetric simple exclusion; tagged particle; fluctuations; systems

摘要

Some invariance principles for additive functionals of simple exclusion with finite-range translation-invariant jump rates p(i, j) = p(j - i) in dimensions d greater than or equal to 1 are established. A previous investigation concentrated on the case of p symmetric. The principal tools to take care of nonreversibility, when p is asymmetric, are invariance principles for associated random variables and a local balance estimate on the asymmetric generator of the process. As a by-product, we provide upper and lower bounds on some transition probabilities for mean-zero asymmetric second-class particles, which are not Markovian, that show they behave like their symmetric Markovian counterparts. Also some estimates with respect to second-class particles with drift are discussed. In addition, a dichotomy between the occupation time process limits in d = 1 and d greater than or equal to 2 for symmetric exclusion is shown. In the former, the limit is fractional Brownian motion with parameter 3/4, and in the latter, the usual Brownian motion.