Asymptotics for the size of the largest component scaled to "log n" in inhomogeneous random graphs

Details Asymptotics for the size of the largest component scaled to "log n" in inhomogeneous random graphs Asymptotics for the size of the largest component scaled to "log n" in inhomogeneous random graphs

2008-12-16

arxiv.org/abs/0812.3007v1

Mathematics

Probability

34 pages

Scientific paper

We study the inhomogeneous random graphs in the subcritical case. We derive an exact formula for the size of the largest connected component scaled to $\log n$ where $n$ is the size of the graph. This generalizes the recent result for the "rank 1 case". Here we discover that the same well-known equation for the survival probability, whose positive solution determines the asymptotics of the size of the largest component in the supercritical case, plays the crucial role in the subcritical case as well. But now these are the negative solutions which come into play.

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