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Planar lattices do not recover from forest fires

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Consider supercritical (p > p_c) site percolation on Z^2. Destroy the infinite open cluster, that is, make all its vertices closed. Then open the closed vertices independently from each other with probability delta. Let theta(p,delta) denote the probability that the origin is in an infinite cluster in the configuration thus obtained. We show that there is a positive delta such that theta(p,delta) = 0 for all p > p_c. This is a joint work with Ioan Manolescu and Vladas Sidoravicius.

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