Screening Effect Due to Heavy Lower Tails in One-Dimensional Parabolic Anderson Model期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Screening Effect Due to Heavy Lower Tails in One-Dimensional Parabolic Anderson Model

Authors:	Marek Biskup Wolfgang König

Institution:	(1) Microsoft Research, One Microsoft Way, Redmond, Washington, 98052;(2) Fachbereich Mathematik MA7-5, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany

Abstract:	We consider the large-time behavior of the solution $u:0,\infty ) \times \mathbb{Z} \to 0,\infty )$ to the parabolic Anderson problem _tu=u+u with initial data u(0, ·)=1 and non-positive finite i.i.d. potentials $(\xi (z))_{z \in \mathbb{Z}}$ . Unlike in dimensions d2, the almost-sure decay rate of u(t, 0) as t is not determined solely by the upper tails of (0); too heavy lower tails of (0) accelerate the decay. The interpretation is that sites x with large negative (x) hamper the mass flow and hence screen off the influence of more favorable regions of the potential. The phenomenon is unique to d=1. The result answers an open question from our previous study BK00] of this model in general dimension.

Keywords:	parabolic Anderson model almost-sure asymptotics large deviations Dirichlet eigenvalues screening effect
本文献已被 SpringerLink 等数据库收录！