Scaling limits for critical inhomogeneous random graphs with finite third moments
Shankar Bhamidi, University of North Carolina
Remco van der Hofstad, Eindhoven University of Technology
Johan S.H. van Leeuwaarden, Eindhoven University of Technology
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 Erdős-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.
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