2005/09/10 by Béla Bollobás, Bela Bollobas, Oliver Riordan
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60K35 #msc:82B43
paper · pdf · doi:10.1016/j.ejc.2006.05.022
published as Europ. J. Combin. 28 (2007), 1720-1723. · 4 pages; author list changed, acknowledgement added
arxiv created 2005/09/10 · openalex publication_date 2007/03/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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.