Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction

• 成果类型: Article
• 署名作者: Rassoul-Agha, Firas; Seppalaineni, Timo
• 署名单位: Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000610
• 发表日期: 2007
• 页码: 1-31
• 关键词: time random environment; central-limit-theorem; additive-functionals; markov-chains

摘要

We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The assumptions are nonnestling, at least two spatial dimensions, and a 2 + epsilon moment for the step of the walk uniformly in the environment. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.