# Scaling limits for critical inhomogeneous random graphs with finite third moments - Mathematics > Probability

Scaling limits for critical inhomogeneous random graphs with finite third moments - Mathematics > Probability - Download this document for free, or read online. Document in PDF available to download.

Abstract: We identify the scaling limits for the sizes of the largest components atcriticality for inhomogeneous random graphs when the degree exponent $\tau$satisfies $\tau>4$. We see that the sizes of the rescaled components convergeto the excursion lengths of an inhomogeneous Brownian motion, extending resultsof \cite{Aldo97}. We rely heavily on martingale convergence techniques, andconcentration properties of supermartingales. This paper is part of aprogramme to study the critical behavior in inhomogeneous random graphs ofso-called rank-1 initiated in \cite{Hofs09a}.

Author: Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden

Source: https://arxiv.org/

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