Novel scaling limits for critical inhomogeneous random graphs

Research output: Contribution to journalArticleAcademicpeer-review

30 Citations (Scopus)
105 Downloads (Pure)

Abstract

We find scaling limits for the sizes of the largest components at criticality for rank-1 inhomogeneous random graphs with power-law degrees with power-law exponent t. We investigate the case where t¿(3,4), so that the degrees have finite variance but infinite third moment. The sizes of the largest clusters, rescaled by n-(t-2)/(t-1), converge to hitting times of a "thinned" Lévy process, a special case of the general multiplicative coalescents studied by Aldous [Ann. Probab. 25 (1997) 812–854] and Aldous and Limic [Electron. J. Probab. 3 (1998) 1–59]. Our results should be contrasted to the case t>4, so that the third moment is finite. There, instead, the sizes of the components rescaled by n-2/3 converge to the excursion lengths of an inhomogeneous Brownian motion, as proved in Aldous [Ann. Probab. 25 (1997) 812–854] for the Erdos–Rényi random graph and extended to the present setting in Bhamidi, van der Hofstad and van Leeuwaarden [Electron. J. Probab. 15 (2010) 1682–1703] and Turova [(2009) Preprint].
Original languageEnglish
Pages (from-to)2299-2361
JournalThe Annals of Probability
Volume40
Issue number6
DOIs
Publication statusPublished - 2012

Fingerprint Dive into the research topics of 'Novel scaling limits for critical inhomogeneous random graphs'. Together they form a unique fingerprint.

Cite this