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Abstract: H\-aggstr\-om, Peres, and Steif (1997) have introduced a dynamical version ofpercolation on a graph $G$. When $G$ is a tree they derived a necessary andsufficient condition for percolation to exist at some time $t$. In the casethat $G$ is a spherically symmetric tree, H\-aggstr\-om, Peres, and Steif(1997) derived a necessary and sufficient condition for percolation to exist atsome time $t$ in a given target set $D$. The main result of the present paperis a necessary and sufficient condition for the existence of percolation, atsome time $t\in D$, in the case that the underlying tree is not necessaryspherically symmetric. This answers a question of Yuval Peres (personalcommunication). We present also a formula for the Hausdorff dimension of theset of exceptional times of percolation.



Autor: Davar Khoshnevisan

Fuente: https://arxiv.org/







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