On near-critical and dynamical percolation in the tree case. (English) Zbl 0945.60093
Let \(G\) be a symmetric tree with root \(\rho\), let \(\theta(p)\) be the probability that the root is in an infinite open cluster and denote by \(p_c\) the critical percolation probability. If \(\theta(p_c)=0\), the root \(\rho\) may still percolate in the corresponding dynamical percolation process at \(p_c\). A necessary and sufficient condition for percolation is given in terms of the function \(\theta\).
Reviewer: Ulrich Horst (Berlin)
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 82C43 | Time-dependent percolation in statistical mechanics |
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