Critical large deviations of one-dimensional annealed Brownian motion in a Poissonian potential

• 成果类型: Article
• 署名作者: Povel, T
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1023481109
• 发表日期: 1997
• 页码: 1735-1773
• 关键词: wiener sausage; asymptotics; drift

摘要

We derive a large deviation principle for the position at large times t of a one-dimensional annealed Brownian motion in a Poissonian potential in the critical spatial scale t(1/3). Here annealed means that averages are taken with respect to both the path and environment measures. In contrast to the d-dimensional case for d greater than or equal to 2 in. the critical scale t(d/(d + 2)) as treated by Sznitman, the rate function which measures the large deviations exhibits three different regimes. These regimes depend on the position of the path at time t. Our large deviation principle has a natural application to the study of a one-dimensional annealed Brownian motion with a constant drift in a Poissonian potential.