BROWNIAN-MOTION IN A POISSONIAN POTENTIAL
成果类型：
Article
署名作者：
SZNITMAN, AS
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/BF01192959
发表日期：
1993
页码：
447-477
关键词：
摘要：
We study here a d-dimensional Brownian motion in a random potential V(.,omega) obtained as the sum of translations of a given fixed non negative shape function at the points of a Poisson cloud of constant intensity nu. We are interested in the large t behavior for typical cloud configurations, of the Brownian path in time t under the influence of the natural Feynman-Kac weight associated to V(.,omega). In particular, we show that the location at time t of the process tends to be concentrated near points of suitably ''low local eigenvalue'' of - 1/2 Delta + V(.,omega), which lie almost at distance t from the origin. Near these points one can find in the cloud a ''big hole'' or ''clearing'' of size similar to const(log t)(1/d) with volume like a ball of radius R(0)(d, nu)(log t)(1/d).