标题： 一维抛物型安德森模型中由于较重下尾产生的筛选效应 显示英文标题

标题： Screening effect due to heavy lower tails in one-dimensional parabolic Anderson model

摘要： 我们考虑抛物线安德森问题 $\partial_t u=\kappa\Delta u+\xi u$ 的解 $u\colon [0,\infty)\times\Z\to[0,\infty)$ 在长时间行为，初始数据为 $u(0,\cdot)=1$ 和非正有限独立同分布的势能 $(\xi(z))_{z\in\Z}$。 与维度$d\ge2$不同，当$t\to\infty$时，$u(t,0)$的几乎必然衰减率不仅仅由$\xi(0)$的上尾决定；$\xi(0)$的过重下尾会加速衰减。 解释是，具有较大负值$\xi(x)$的站点$x$会阻碍质量流动，因此屏蔽了势能更有利区域的影响。 这一现象仅在$d=1$中出现。 该结果回答了我们之前在一般维度下对该模型的先前研究\cite{BK00}中的一个开放问题。 显示英文摘要

摘要： We consider the large-time behavior of the solution $u\colon [0,\infty)\times\Z\to[0,\infty)$ to the parabolic Anderson problem $\partial_t u=\kappa\Delta u+\xi u$ with initial data $u(0,\cdot)=1$ and non-positive finite i.i.d. potentials $(\xi(z))_{z\in\Z}$. Unlike in dimensions $d\ge2$, the almost-sure decay rate of $u(t,0)$ as $t\to\infty$ is not determined solely by the upper tails of $\xi(0)$; too heavy lower tails of $\xi(0)$ accelerate the decay. The interpretation is that sites $x$ with large negative $\xi(x)$ 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 \cite{BK00} of this model in general dimension.