Dynamical percolation on general trees
| dc.creator | Khoshnevisan, Davar | |
| dc.date | 2007-05-01 | |
| dc.date.accessioned | 2026-07-07T07:58:56Z | |
| dc.date.available | 2026-07-07T07:58:56Z | |
| dc.description | Häggström, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, Häggström, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation. | |
| dc.description | 24 pages; to appear in Probability Theory and Related Fields | |
| dc.identifier | https://arxiv.org/abs/0705.0140 | |
| dc.identifier | http://arxiv.org/abs/0705.0140 | |
| dc.identifier | doi:10.1007/s00440-007-0061-6 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128186 | |
| dc.subject | Probability | |
| dc.subject | Primary. 60K35; Secondary. 31C15, 60J45 | |
| dc.title | Dynamical percolation on general trees | |
| dc.type | text |