Tatjana Turova Schmeling

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

Abstract

We shall consider the inhomogeneous random graphs. 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. In particular, 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.

(Specialists on non-linear operators are particularly welcome.)