Screening effect due to heavy lower tails in one-dimensional parabolic Anderson model
Biskup, Marek ; Koenig, Wolfgang
arXiv, 0007013 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-07-10
Classification:  Mathematical Physics,  Mathematics - Probability,  60F10,  35B40,  35K15 
@article{0007013,
     author = {Biskup, Marek and Koenig, Wolfgang},
     title = {Screening effect due to heavy lower tails in one-dimensional parabolic
  Anderson model},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0007013}
}

Biskup, Marek; Koenig, Wolfgang. Screening effect due to heavy lower tails in one-dimensional parabolic
  Anderson model. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0007013/