Fluctuations in the occupation time of a site in the asymmetric simple exclusion process

• 成果类型: Article
• 署名作者: Bernardin, C
• 署名单位: Universite Paris Saclay
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1079021466
• 发表日期: 2004
• 页码: 855-879
• 关键词: additive-functionals; tagged particle; limit

摘要

We consider the simple asymmetric exclusion process with nonzero drift under the stationary Bernoulli product measure at density rho. We prove that for dimension d = 2 the occupation time of the site 0 is diffusive as soon as rho not equal 1/2. For dimension d = 1, if the density rho is equal to 1/2, we prove that the time t variance of the occupation time of the site 0 diverges in a certain sense at least as t(5/4).