@article{EJP817,
author = {Shankar Bhamidi and Remco van der Hofstad and Johan van Leeuwaarden},
title = {Scaling Limits for Critical Inhomogeneous Random Graphs with Finite Third Moments},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {15},
year = {2010},
keywords = {critical random graphs; phase transitions; inhomogeneous networks; Brownian excursions; size-biased ordering; martingale techniques},
abstract = {We identify the scaling limit for the sizes of the largest components at criticality for inhomogeneous random graphs with weights that have finite third moments. We show that the sizes of the (rescaled) components converge to the excursion lengths of an inhomogeneous Brownian motion, which extends results of Aldous (1997) for the critical behavior of Erdös-Rényi random graphs. We rely heavily on martingale convergence techniques, and concentration properties of (super)martingales. This paper is part of a programme initiated in van der Hofstad (2009) to study the near-critical behavior in inhomogeneous random graphs of so-called rank-1.},
pages = {no. 54, 1682-1702},
issn = {1083-6489},
doi = {10.1214/EJP.v15-817},
url = {http://ejp.ejpecp.org/article/view/817}}