Sharp threshold for percolation on expanders
Seminar Room 1, Newton Institute
AbstractIn 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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