Scaling identity for crossing Brownian motion in a Poissonian potential

被引：13

作者：

Wuthrich, MV ^{[1
]}

机构：

[1] ETH Zentrum, Dept Math, CH-8092 Zurich, Switzerland

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1998年 / 112卷 / 03期

关键词：

D O I：

10.1007/s004400050192

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider d-dimensional Brownian motion in a truncated Poissonian potential (d greater than or equal to 2). If Brownian motion starts at the origin and ends in the closed ball with center y and radius 1, then the transverse fluctuation of the path is expected to be of order \y\(xi), whereas the distance fluctuation is of order \y\(chi). Physics literature tells us that xi and chi should satisfy a scaling identity 2 xi - 1 = chi. We give here rigorous results for this conjecture.

引用

页码：299 / 319

页数：21

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