We give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice Z2 is equal to 1/2. The lower bound was proved by Harris, who showed in 1960 that percolation does not occur at p = 1/2. The other, more difficult, bound was proved by Kesten, who showed in 1980 that percolation does occur for any p > 1/2. 2000 Mathematics Subject Classification 60K35, 82B43.
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