Superdiffusive behavior of two-dimensional Brownian motion in a Poissonian potential

• 成果类型: Article
• 署名作者: Wuthrich, MV
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 1000-1015
• 关键词: lyapounov exponents; fluctuations; impurities

摘要

We consider d-dimensional Brownian motion in a truncated Poissonian potential conditioned to reach a remote location. If Brownian motion starts at the origin and ends in an hyperplane at distance L from the origin, the transverse fluctuation of the path is expected to be of order L-xi. We are interested in a lower bound for xi. We first show that xi greater than or equal to 1/2 in dimensions d greater than or equal to 2 and then we prove superdiffusive behavior for d = 2, resulting in xi greater than or equal to 3/5.