A note on the Harris-Kesten Theorem
Probability
2009-05-08 v2
Abstract
Recently, a short proof of the Harris-Kesten result that the critical probability for bond percolation in the planar square lattice is 1/2 was given, using a sharp threshold result of Friedgut and Kalai. Here we point out that a key part of this proof may be replaced by an argument of Russo from 1982, using his approximate zero-one law in place of the Friedgut-Kalai result. Russo's paper gave a new proof of the Harris-Kesten Theorem that seems to have received little attention.
Cite
@article{arxiv.math/0509131,
title = {A note on the Harris-Kesten Theorem},
author = {Bela Bollobas and Oliver Riordan},
journal= {arXiv preprint arXiv:math/0509131},
year = {2009}
}
Comments
4 pages; author list changed, acknowledgement added