A moment-generating formula for Erdős-Rényi component sizes

Abstract

We derive a simple formula characterizing the distribution of the size of the connected component of a fixed vertex in the Erdős-Rényi random graph which allows us to give elementary proofs of some results of Federico, van der Hofstad, den Hollander and Hulshof as well as Janson and Luczak about the susceptibility in the subcritical graph and the central limit theorem of Pittel for the size of the giant component in the supercritical graph.

14 pages

References in corpus (4)

• Susceptibility in subcritical random graphs
• Rigid representations of the multiplicative coalescent with linear deletion
• Expansion of percolation critical points for Hamming graphs
• A multiplicative coalescent with asynchronous multiple mergers

Cited by in corpus (3)

• Expansion of percolation critical points for Hamming graphs
• Distribution of outbreak sizes for SIR disease in finite populations
• A multiplicative coalescent with asynchronous multiple mergers