Singularity points for first passage percolation
| dc.creator | Yukich, J. E. | |
| dc.creator | Zhang, Yu | |
| dc.date | 2005-06-13 | |
| dc.date | 2006-05-24 | |
| dc.date.accessioned | 2026-07-07T06:42:24Z | |
| dc.date.available | 2026-07-07T06:42:24Z | |
| dc.description | Let $0<a<b<\infty$ be fixed scalars. Assign independently to each edge in the lattice $\mathbb{Z}^2$ the value $a$ with probability $p$ or the value $b$ with probability $1-p$. For all $u,v\in\mathbb{Z}^2$, let $T(u,v)$ denote the first passage time between $u$ and $v$. We show that there are points $x\in\mathbb{R}^2$ such that the ``time constant'' in the direction of $x$, namely, $\lim_{n\to\infty}n^{-1}\mathbf{E}_p[T(\mathbf{0},nx)],$ is not a three times differentiable function of $p$. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117905000000819 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0506241 | |
| dc.identifier | http://arxiv.org/abs/math/0506241 | |
| dc.identifier | Annals of Probability 2006, Vol. 34, No. 2, 577-592 | |
| dc.identifier | doi:10.1214/009117905000000819 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102030 | |
| dc.subject | Probability | |
| dc.subject | 60K35 (Primary) | |
| dc.title | Singularity points for first passage percolation | |
| dc.type | text |