Long-time tails in the parabolic Anderson model with bounded potential
| dc.creator | Biskup, Marek | |
| dc.creator | Koenig, Wolfgang | |
| dc.date | 2000-04-12 | |
| dc.date | 2003-09-30 | |
| dc.date.accessioned | 2026-07-07T04:27:46Z | |
| dc.date.available | 2026-07-07T04:27:46Z | |
| dc.description | We consider the parabolic Anderson problem $\partial_t u=κΔu+ξu$ on $(0,\infty)\times \Z^d$ with random i.i.d. potential $ξ=(ξ(z))_{z\in\Z^d}$ and the initial condition $u(0,\cdot)\equiv1$. Our main assumption is that $\esssupξ(0)=0$. Depending on the thickness of the distribution $\prob(ξ(0)\in\cdot)$ close to its essential supremum, we identify both the asymptotics of the moments of $u(t,0)$ and the almost-sure asymptotics of $u(t,0)$ as $t\to\infty$ in terms of variational problems. As a by-product, we establish Lifshitz tails for the random Schrödinger operator $-κΔ-ξ$ at the bottom of its spectrum. In our class of $ξ$ distributions, the Lifshitz exponent ranges from $d/2$ to $\infty$; the power law is typically accompanied by lower-order corrections. | |
| dc.description | 40 pages, LaTeX 2e+times, version published in Ann. Probab | |
| dc.identifier | https://arxiv.org/abs/math-ph/0004014 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0004014 | |
| dc.identifier | Ann. Probab. 29 (2001), no. 2, 636-682 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56538 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.subject | 60F10; 82B44; 35B40; 35K15 | |
| dc.title | Long-time tails in the parabolic Anderson model with bounded potential | |
| dc.type | text |