A short proof of the Harris-Kesten theorem

Abstract

We give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice ℤ 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. © 2006 London Mathematical Society.