Open Access
January 2012 Sharp threshold for percolation on expanders
Itai Benjamini, Stéphane Boucheron, Gábor Lugosi, Raphaël Rossignol
Ann. Probab. 40(1): 130-145 (January 2012). DOI: 10.1214/10-AOP610


We study the appearance of the giant component in random subgraphs of a given large finite graph G = (V, E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c ∈ ]0, 1[, the property that the random subgraph contains a giant component of size c|V| has a sharp threshold.


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Itai Benjamini. Stéphane Boucheron. Gábor Lugosi. Raphaël Rossignol. "Sharp threshold for percolation on expanders." Ann. Probab. 40 (1) 130 - 145, January 2012.


Published: January 2012
First available in Project Euclid: 3 January 2012

zbMATH: 1239.60090
MathSciNet: MR2917769
Digital Object Identifier: 10.1214/10-AOP610

Primary: 05C80 , 60K35

Keywords: expander , Giant component , percolation , random graph , sharp threshold

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 1 • January 2012
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