 00288 Marek Biskup and Wolfgang Koenig
 Screening effect due to heavy lower tails in onedimensional
parabolic Anderson model
(1368K, LaTeX & Postscript)
Jul 10, 00

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We consider the largetime 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 nonpositive finite i.i.d.\ potentials $(\xi(z))_{z\in\Z}$. Unlike in dimensions $d\ge2$, the almostsure 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.
 Files:
00288.src(
00288.keywords ,
1DpAmfinal.tex ,
1DpAmfinal.ps )