Sharp threshold for percolation on expanders

• Autores: Itai Benjamini, Stéphane Boucheron, Gábor Lugosi, Raphaël Rossignol
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 40, Nº. 1, 2012, págs. 130-145
• Idioma: inglés
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• Resumen

  • 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.