Annals of Probability

Sharp threshold for percolation on expanders

Itai Benjamini, Stéphane Boucheron, Gábor Lugosi, and Raphaël Rossignol

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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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Ann. Probab., Volume 40, Number 1 (2012), 130-145.

First available in Project Euclid: 3 January 2012

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 05C80: Random graphs [See also 60B20]

Percolation random graph expander giant component sharp threshold


Benjamini, Itai; Boucheron, Stéphane; Lugosi, Gábor; Rossignol, Raphaël. Sharp threshold for percolation on expanders. Ann. Probab. 40 (2012), no. 1, 130--145. doi:10.1214/10-AOP610.

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