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.
On the uniqueness of the infinite cluster in the percolation model / A. Gandolfi;G. Grimmett;L. Russo. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 114:(1988), pp. 549-552. [10.1007/BF01229454]
On the uniqueness of the infinite cluster in the percolation model
GANDOLFI, ALBERTO;
1988
Abstract
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.
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