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Sharp threshold for percolation on expanders

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arxiv 0906.3657 v2 pith:RWKEUL44 submitted 2009-06-19 math.PR

Itai Benjamini , Stéphane Boucheron , Gábor Lugosi , Raphaël Rossignol This is my paper · ORCID
classification math.PR
keywords componentgiantrandomsharpthresholdappearanceboundedcontains
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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 in ]0,1[, the property that the random subgraph contains a giant component of size c|V| has a sharp threshold.

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