Large deviation principle for random walk in a quenched random environment in the low speed regime

• 成果类型: Article
• 署名作者: Pisztora, A; Povel, T
• 署名单位: Carnegie Mellon University; Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1999
• 页码: 1389-1413
• 关键词: dimensional random-walk; brownian-motion

摘要

We consider a one-dimensional random walk (X-n)(n x N) in a random environment of zero or strictly positive drifts. We establish a full large deviation principle for X-n/n of the correct order n/(log n)(2) in the low speed regime, valid for almost every environment. This completes the large deviation picture obtained earlier by Greven and den Hollander and Gantert and Zeitouni in the case of zero and positive drifts. The proof uses coarse graining along with concentration of measure techniques.