A universality property for last-passage percolation paths close to the axis
| dc.creator | Bodineau, Thierry | |
| dc.creator | Martin, James B. | |
| dc.date | 2004-10-03 | |
| dc.date.accessioned | 2026-07-07T05:12:49Z | |
| dc.date.available | 2026-07-07T05:12:49Z | |
| dc.description | We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the origin to the point $\big(n,n^{\lfloor a \rfloor}\big)$. We show that, for suitable $a$ (depending on $p$), this quantity, appropriately scaled, converges in distribution as $n\to\infty$ to the Tracy-Widom distribution, irrespective of the underlying weight distribution. The argument uses a coupling to a Brownian directed percolation problem and the strong approximation of Komlós, Major and Tusnády. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0410042 | |
| dc.identifier | http://arxiv.org/abs/math/0410042 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72720 | |
| dc.subject | Probability | |
| dc.subject | 60K35 | |
| dc.title | A universality property for last-passage percolation paths close to the axis | |
| dc.type | text |