Moment asymptotics for the continuous parabolic Anderson model

• 成果类型: Article
• 署名作者: Gärtner, J; König, W
• 署名单位: Technical University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1019737669
• 发表日期: 2000
• 页码: 192-217
• 关键词: intermittency

摘要

We consider the parabolic Anderson problem partial derivative (t)u = kappa Deltau + xi (x)u on R+ x R-d with initial condition u(0, x) = 1. Here xi(.) is a random shift-invariant potential having high delta -like peaks on small islands. We express the second-order asymptotics of the pth moment (p is an element of [1, infinity)) of u(t, 0) as t --> infinity in terms of a variational formula involving an asymptotic description of the rescaled shapes of these peaks via their cumulant generating function. This includes Gaussian potentials and high Poisson clouds.