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document
Gandolfi, A. (author), Keane, M. (author), Russo, L. (author)
We consider dependent site percolation on the two-dimensional square lattice, the underlying probability measure being invariant and ergodic under each of the translations and invariant under axis reflections. If this measure satisfies the FKG condition and if percolation occurs, then we show that the infinite occupied cluster is unique with...
journal article 1988
document
Gandolfi, A. (author), Grimmett, G. (author), Russo, L. (author)
We simplify the recent proof by Aizenman, Kesten and Newman of the uniqueness of the infinite open cluster in the percolation model. Our new proof is more suitable for generalization in the direction of percolation-type processes with dependent site variables.
journal article 1987