We identify the scaling limits for the sizes of the largest components at criticality for inhomogeneous random graphs when the degree exponent r satisfies r > 4. We see that the sizes of the (rescaled) components converge to the excursion lengths of an inhomogeneous Brownian motion, extending results of . 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 .
|Status||Gepubliceerd - 2009|