Distance fluctuations and Lyapounov exponents
成果类型：
Article
署名作者：
Sznitman, AS
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1065725191
发表日期：
1996
页码：
1507-1530
关键词：
摘要：
We associate certain translation invariant random metrics on R(d) to Brownian motion evolving in a truncated Poissonian potential. These metrics behave over large distances, in an appropriate sense, like certain deterministic norms (the so-called Lyapounov exponents). We prove here upper bounds on the size of fluctuations of the metrics around their mean. Under an additional assumption of rotational invariance, we also derive upper bounds on the difference between the mean of the metrics and the Lyapounov norms.