Sur le nombre de points visités par une marche aléatoire sur un amas infini de percolation
| dc.creator | Rau, Clement | |
| dc.date | 2006-05-02 | |
| dc.date.accessioned | 2026-07-07T07:13:50Z | |
| dc.date.available | 2026-07-07T07:13:50Z | |
| dc.description | In this article, we consider random walk on the infinite cluster of bond percolation on $\Z^d (d \geq 2)$. We show that the Laplace transformation of the number of visited points $N\_n$, has a behaviour as the random walk was on $\Z^d$. More precisely, for all $0<α<1$, we proved that there exist constants $C\_i$ and $C\_s$ such that for all infinite cluster that contains the origin, we have: $$ e^{-C\_i n^{\frac{d}{d+2}}} \leq \E\_0^ω (α^{N\_n}) \leq e^{-C\_sn^{\frac{d}{d+2}}}.$$ Our approach is based on finding an isoperimetric inequalities on the infinite cluster, lifted on a wreath product which give good behaviour. The problem of the isoperimetry on wreath product was already raised by A.Ershler. | |
| dc.description | 38 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0605056 | |
| dc.identifier | http://arxiv.org/abs/math/0605056 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112627 | |
| dc.subject | Probability | |
| dc.title | Sur le nombre de points visités par une marche aléatoire sur un amas infini de percolation | |
| dc.type | text |