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arXiv:math/0410359 [math.PR]AbstractReferencesReviewsResources

A short proof of the Harris-Kesten Theorem

Bela Bollobas, Oliver Riordan

Published 2004-10-15, updated 2005-06-16Version 3

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 $p>1/2$.

Comments: 17 pages, 9 figures; typos corrected. To appear in the Bulletin of the London Mathematical Society
Journal: Bulletin of the London Mathematical Society 38 (2006), 470--484.
Categories: math.PR, math.CO
Subjects: 60K35, 82B43
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