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Kesten showed the exponential decay of percolation probability in thesubcritical phase for the two-dimensional percolation model. This resultimplies his celebrated computation that $p_c=0.5$ for bond percolation in thesquare lattice, and site percolation in the triangular lattice, respectively.In this paper, we present a simpler proof for Kesten's theorem.

A simple proof of exponential decay in the two dimensional percolation model