Transient random walks on 2d-oriented lattices
| dc.creator | Guillotin-Plantard, Nadine | |
| dc.creator | Ny, Arnaud Le | |
| dc.date | 2006-01-05 | |
| dc.date.accessioned | 2026-07-07T06:58:34Z | |
| dc.date.available | 2026-07-07T06:58:34Z | |
| dc.description | We study the asymptotic behavior of the simple random walk on oriented versions of $\mathbb{Z}^2$. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, with random orientations whose distributions are generated by a dynamical system. We find a sufficient condition on the smoothness of the generation for the transience of the simple random walk on almost every such oriented lattices, and as an illustration we provide a wide class of examples of inhomogeneous or correlated distributions of the orientations. For ergodic dynamical systems, we also prove a strong law of large numbers and, in the particular case of i.i.d. orientations, we solve an open problem and prove a functional limit theorem in a corresponding space D of cadlag functions, with an unconventional normalization. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601102 | |
| dc.identifier | http://arxiv.org/abs/math/0601102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107403 | |
| dc.subject | Probability | |
| dc.subject | Dynamical Systems | |
| dc.subject | 60K37; 60F17; 60K35 | |
| dc.title | Transient random walks on 2d-oriented lattices | |
| dc.type | text |