A quenched limit theorem for the local time of random walks on \Z^2
| dc.creator | Gärtner, Jürgen | |
| dc.creator | Sun, Rongfeng | |
| dc.date | 2007-11-28 | |
| dc.date | 2008-06-10 | |
| dc.date.accessioned | 2026-07-07T09:43:11Z | |
| dc.date.available | 2026-07-07T09:43:11Z | |
| dc.description | Let $X$ and $Y$ be two independent random walks on $\Z^2$ with zero mean and finite variances, and let $L_t(X,Y)$ be the local time of $X-Y$ at the origin at time $t$. We show that almost surely with respect to $Y$, $L_t(X,Y)/\log t$ conditioned on $Y$ converges in distribution to an exponential random variable with the same mean as the distributional limit of $L_t(X,Y)/\log t$ without conditioning. This question arises naturally from the study of the parabolic Anderson model with a single moving catalyst, which is closely related to a pinning model. | |
| dc.description | To appear in Stochastic Processes and Their Applications. Updated version. 16 pages. Added discussion on d=1 and d\geq 3 as well as an open problem | |
| dc.identifier | https://arxiv.org/abs/0711.4488 | |
| dc.identifier | http://arxiv.org/abs/0711.4488 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162461 | |
| dc.subject | Probability | |
| dc.subject | 60J15 (Primary) 60K37, 60J55, 60F05 (Secondary) | |
| dc.title | A quenched limit theorem for the local time of random walks on \Z^2 | |
| dc.type | text |