BROWNIAN SURVIVAL AMONG GIBBSIAN TRAPS

• 成果类型: Article
• 署名作者: SZNITMAN, AS
• 署名单位: New York University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989413
• 发表日期: 1993
• 页码: 490-508
• 关键词: wiener sausage; asymptotics

摘要

We consider Brownian motion evolving among killing traps. We develop a technique of ''enlargement of obstacles.'' This technique allows us to replace given trap configurations by configurations of enlarged traps, when deriving upper estimates on the probability that Brownian motion survives. Applied in a context of random obstacles, this reduces the complexity of the description for the environment seen by Brownian motion. We apply the method to the case where traps are distributed according to a fairly general Gibbs measure and obtain a result in the spirit of Donsker-Varadhan's theorem on Wiener sausage asymptotics.