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2010 Scaling Limits for Critical Inhomogeneous Random Graphs with Finite Third Moments
Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden
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Electron. J. Probab. 15: 1682-1702 (2010). DOI: 10.1214/EJP.v15-817

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.

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Shankar Bhamidi. Remco van der Hofstad. Johan van Leeuwaarden. "Scaling Limits for Critical Inhomogeneous Random Graphs with Finite Third Moments." Electron. J. Probab. 15 1682 - 1702, 2010. https://doi.org/10.1214/EJP.v15-817

Information

Accepted: 2 November 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1228.60018
MathSciNet: MR2735378
Digital Object Identifier: 10.1214/EJP.v15-817

Subjects:
Primary: 60C05
Secondary: 05C80, 90B15

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Vol.15 • 2010
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