Screening effect due to heavy lower tails in one-dimensional parabolic Anderson model
| dc.creator | Biskup, Marek | |
| dc.creator | Koenig, Wolfgang | |
| dc.date | 2000-07-10 | |
| dc.date.accessioned | 2026-07-07T04:27:53Z | |
| dc.date.available | 2026-07-07T04:27:53Z | |
| dc.description | We consider the large-time behavior of the solution $u\colon [0,\infty)\times\Z\to[0,\infty)$ to the parabolic Anderson problem $\partial_t u=κΔu+ξu$ with initial data $u(0,\cdot)=1$ and non-positive finite i.i.d. potentials $(ξ(z))_{z\in\Z}$. 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 $ξ(0)$; too heavy lower tails of $ξ(0)$ accelerate the decay. The interpretation is that sites $x$ with large negative $ξ(x)$ 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. | |
| dc.description | LaTeX+times package, 14 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0007013 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0007013 | |
| dc.identifier | J. Statist. Phys. 102 (2001), no. 5/6, 1253-1270. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56582 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.subject | 60F10; 35B40; 35K15 | |
| dc.title | Screening effect due to heavy lower tails in one-dimensional parabolic Anderson model | |
| dc.type | text |