On the uniqueness of the infinite cluster in the percolation model (Q1105927)

The uniqueness of the infinite open cluster of the percolation model has been conjectured for a long time, and was proved recently by \textit{M. Aizenman}, \textit{H. Kesten} and \textit{C. M. Newman} [see Percolation theory and ergodic theory of infinite particle systems, Proc. Workshop IMA, Minneapolis/Minn. 1984/85, IMA Vol. Math. Appl. 8, 13-20 (1987; Zbl 0621.60112)]. In this paper, the authors present a simplified proof. The new approach is more suitable for a generalization in some directions.