On near-critical and dynamical percolation in the tree case
| dc.creator | Haggstrom, Olle | |
| dc.creator | Pemantle, Robin | |
| dc.date | 2004-04-05 | |
| dc.date.accessioned | 2026-07-07T05:07:08Z | |
| dc.date.available | 2026-07-07T05:07:08Z | |
| dc.description | Consider independent bond percolation with retention probability p on a spherically symmetric tree Gamma. Write theta_Gamma(p) for the probability that the root is in an infinite open cluster, and define the critical value p_c=inf{p:theta_Gamma(p)>0}. If theta_Gamma(p_c)=0, then the root may still percolate in the corresponding dynamical percolation process at the critical value p_c, as demonstrated recently by Haggstrom, Peres and Steif. Here we relate this phenomenon to the near-critical behaviour of theta_Gamma(p) by showing that the root percolates in the dynamical percolation process if and only if int_{p_c}^1 (theta_Gamma(p))^{-1}dp<infty. The ``only if'' direction extends to general trees, whereas the ``if'' direction fails in this generality. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404091 | |
| dc.identifier | http://arxiv.org/abs/math/0404091 | |
| dc.identifier | Rand. Struct. Alg., 15, 311 - 318 (1999) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70740 | |
| dc.subject | Probability | |
| dc.title | On near-critical and dynamical percolation in the tree case | |
| dc.type | text |