Coincidence of Lyapunov exponents for random walks in weak random potentials

• 成果类型: Article
• 署名作者: Flury, Markus
• 署名单位: University of Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/00-AOP368
• 发表日期: 2008
• 页码: 1528-1583
• 关键词: random environment; directed polymers; diffusion

摘要

We investigate the free energy of nearest-neighbor random walks on Z(d), endowed with a drift along the first axis and evolving in a nonnegative random potential given by i.i.d. random variables. Our main result concerns the ballistic regime in dimensions d >= 4, at which we show that quenched and annealed Lyapunov exponents are equal as soon as the strength of the potential is small enough.