A short proof of the Harris-Kesten Theorem
Probability
2007-05-23 v3 Combinatorics
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 . The other, more difficult, bound was proved by Kesten, who showed in 1980 that percolation does occur for any .
Cite
@article{arxiv.math/0410359,
title = {A short proof of the Harris-Kesten Theorem},
author = {Bela Bollobas and Oliver Riordan},
journal= {arXiv preprint arXiv:math/0410359},
year = {2007}
}
Comments
17 pages, 9 figures; typos corrected. To appear in the Bulletin of the London Mathematical Society