CURRENT FLUCTUATIONS OF A SYSTEM OF ONE-DIMENSIONAL RANDOM WALKS IN RANDOM ENVIRONMENT

• 成果类型: Article
• 署名作者: Peterson, Jonathon; Seppaelaeinen, Timo
• 署名单位: Cornell University; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP537
• 发表日期: 2010
• 页码: 2258-2294
• 关键词: transient random-walks; central-limit-theorem; tagged particle; quenched limits; motion

摘要

We study the current of particles that move independently in a common static random environment on the one-dimensional integer lattice. A two-level fluctuation picture appears. On the central limit scale the quenched mean of the current process converges to a Brownian motion. On a smaller scale the current process centered at its quenched mean converges to a mixture of Gaussian processes. These Gaussian processes are similar to those arising from classical random walks, but the environment makes itself felt through an additional Brownian random shift in the spatial argument of the limiting current process.