Brownian confinement and pinning in a Poissonian potential. I
Brownian confinement and pinning in a Poissonian potential. I
复制标题
布朗约束和泊松势的钉扎。
DOI：
10.1007/bf01192069
复制
发表时间：
1996
影响因子：
2
通讯作者：
A. Sznitman
中科院分区：
文献类型：
--
作者：
A. Sznitman
摘要我们研究了在较长时间间隔 [0,t] 内软排斥泊松势中 ad 维布朗运动的行为。我们引入了某些依赖于配置的尺度，其几乎随其线性增长。对于概率趋于 1 ast 到 ∞ 的典型配置，过程位移的大小受这些尺度限制（限制效应）。证明涉及“领先顺序”之外的计算。为此，我们使用环境的粗粒度图片（扩大障碍物的方法）和路径（环境中空地和森林部分之间的游览的主干）。在证明钉扎效应时，这些粗粒度图片也被用在本文的续篇[11]中。
SummaryWe study the behavior of ad dimensional Brownian motion in a soft repulsive Poissonian potential over long time intervals [0,t]. We introduce certaint and configuration dependent scales, which grow almost linearly witht. For typical configurations with probability tending to 1 ast goes to ∞, the size of displacements of the process is bounded above by these scales, (confinement effect). The proof involves calculations beyond “leading order”. To this end we use a coarse grained picture of the environment (method of enlargement of obstacles) and of the path (a backbone of excursions between clearings and forest parts in the environment). These coarse grained pictures are also used in the sequel [11] to the present article, when proving the pinning effect.