Scaling limits for critical inhomogeneous random graphs with finite third moments

Research output: Book/ReportReportAcademic

Abstract

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 [1]. 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 [12].
Original languageEnglish
Publishers.n.
Number of pages19
Publication statusPublished - 2009

Publication series

NamearXiv.org [math.PR]
Volume0907.4279

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