A note on the Harris-Kesten Theorem

Bela Bollobas; Oliver Riordan

doi:10.1016/j.ejc.2006.05.022

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A note on the Harris-Kesten Theorem

Bela Bollobas·Oliver Riordan

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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.

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Bela Bollobas, Oliver Riordan. 2005-09-10. A note on the Harris-Kesten Theorem. https://doi.org/10.1016/j.ejc.2006.05.022

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