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Inequality of Two Critical Probabilities for Percolation

   
@article{ECP1099,
	author = {Jeff Kahn},
	title = {Inequality of Two Critical Probabilities for Percolation},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {8},
	year = {2003},
	keywords = {},
	abstract = {We disprove a conjecture of Russ Lyons---that for every locally finite, connected graph $G$, the critical probability for (Bernoulli bond) percolation on $G$ is equal to the "first moment method" lower bound on this probability---and propose a possible alternative.},
	pages = {no. 21, 184-187},
	issn = {1083-589X},
	doi = {10.1214/ECP.v8-1099},    
        url = {http://ecp.ejpecp.org/article/view/1099}}