Acceleration of Lamplighter Random Walks
| dc.creator | Gilch, Lorenz | |
| dc.date | 2007-08-28 | |
| dc.date | 2008-10-02 | |
| dc.date.accessioned | 2026-07-07T10:06:30Z | |
| dc.date.available | 2026-07-07T10:06:30Z | |
| dc.description | Suppose we are given an infinite, finitely generated group $G$ and a transient random walk on the wreath product $(\mathbb{Z}/ 2\mathbb{Z})\wr G$, such that its projection on $G$ is transient and has finite first moment. This random walk can be interpreted as a lamplighter random walk on $G$. Our aim is to show that the random walk on the wreath product escapes to infinity with respect to a suitable (pseudo-)metric faster than its projection onto $G$. We also address the case where the pseudo-metric is the length of a shortest ``travelling salesman tour''. In this context, and excluding some degenerate cases if $G=\mathbb{Z}$, the linear rate of escape is strictly bigger than the rate of escape of the lamplighter random walk's projection on $G$. | |
| dc.description | 20 pages, accepted for publication in Markov Processes and Related Fields | |
| dc.identifier | https://arxiv.org/abs/0708.3767 | |
| dc.identifier | http://arxiv.org/abs/0708.3767 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170345 | |
| dc.subject | Probability | |
| dc.subject | 60G50 (Primary); 20E22, 60B15 (Secondary) | |
| dc.title | Acceleration of Lamplighter Random Walks | |
| dc.type | text |