%0 Journal Article
%T Scaling limits for critical inhomogeneous random graphs with finite third moments
%A Shankar Bhamidi
%A Remco van der Hofstad
%A Johan van Leeuwaarden
%J Mathematics
%D 2009
%I arXiv
%X We identify the scaling limits for the sizes of the largest components at criticality for inhomogeneous random graphs when the degree exponent $\tau$ satisfies $\tau>4$. We see that the sizes of the (rescaled) components converge to the excursion lengths of an inhomogeneous Brownian motion, extending results of \cite{Aldo97}. We rely heavily on martingale convergence techniques, and concentration properties of (super)martingales. This paper is part of a programme to study the critical behavior in inhomogeneous random graphs of so-called rank-1 initiated in \cite{Hofs09a}.
%U http://arxiv.org/abs/0907.4279v2