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A short proof of the Harris-Kesten Theorem

Bela Bollobas·Oliver Riordan
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Abstract

We give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice 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 $p>1/2$.

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Bela Bollobas, Oliver Riordan. 2005-06-16. A short proof of the Harris-Kesten Theorem. https://doi.org/10.1112/s002460930601842x

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