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Sharp threshold for percolation on expanders

Wednesday 30th March 2011 - 10:00 to 11:00
INI Seminar Room 1
In this joint work with I. Benjamini, S. Boucheron, and R. Rossignol, we study the appearance of the giant component in random subgraphs of a given 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. The main technical tools are based on variance inequalities for functions of independent random variables.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons