Susceptibility in inhomogeneous random graphs

Details Susceptibility in inhomogeneous random graphs Susceptibility in inhomogeneous random graphs

2009-05-04

arxiv.org/abs/0905.0437v1

Electronic J. Combinatorics 19 (2012), P31 (59 pages)

Mathematics

Probability

51 pages

Scientific paper

We study the susceptibility, i.e., the mean size of the component containing a random vertex, in a general model of inhomogeneous random graphs. This is one of the fundamental quantities associated to (percolation) phase transitions; in practice one of its main uses is that it often gives a way of determining the critical point by solving certain linear equations. Here we relate the susceptibility of suitable random graphs to a quantity associated to the corresponding branching process, and study both quantities in various natural examples.

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