Hitting time of large subsets of the hypercube
| dc.creator | Cerny, Jiri | |
| dc.creator | Gayrard, Veronique | |
| dc.date | 2006-11-08 | |
| dc.date.accessioned | 2026-07-07T07:32:39Z | |
| dc.date.available | 2026-07-07T07:32:39Z | |
| dc.description | We study the simple random walk on the $n$-dimensional hypercube, in particular its hitting times of large (possibly random) sets. We give simple conditions on these sets ensuring that the properly-rescaled hitting time is asymptotically exponentially distributed, uniformly in the starting position of the walk. These conditions are then verified for percolation clouds with densities that are much smaller than $(n \log n)^{-1}$. A main motivation behind this paper is the study of the so-called aging phenomenon in the Random Energy Model (REM), the simplest model of a mean-field spin glass. Our results allow us to prove aging in the REM for all temperatures, thereby extending earlier results to their optimal temperature domain. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611242 | |
| dc.identifier | http://arxiv.org/abs/math/0611242 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119187 | |
| dc.subject | Probability | |
| dc.title | Hitting time of large subsets of the hypercube | |
| dc.type | text |