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The supercritical phase of percolation is well behaved

1990; Royal Society; Volume: 430; Issue: 1879 Linguagem: Inglês

10.1098/rspa.1990.0100

2053-9177

Geoffrey Grimmett, J. M. Marstrand,

Markov Chains and Monte Carlo Methods

We prove a general result concerning the critical probabilities of subsets of a lattice L . It is a consequence of this result that the critical probability of a percolation process on L equals the limit of the critical probability of a slice of L as the thickness of the slice tends to infinity. This verification of one of the standard hypotheses of the subject settles many questions concerning supercritical percolation.