Scaling limits for critical inhomogeneous random graphs with finite third moments

被引：44

作者：

Bhamidi, Shankar ^{[1
]}

van der Hofstad, Remco ^{[2
]}

van Leeuwaarden, Johan S. H. ^{[2
]}

机构：

[1] Univ N Carolina, Dept Stat & Operat Res, Chapel Hill, NC 27510 USA

[2] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2010年 / 15卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

critical random graphs; phase transitions; inhomogeneous networks; Brownian excursions; size-biased ordering; martingale techniques; COMPONENT;

D O I：

10.1214/EJP.v15-817

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 [1] for the critical behavior of Erdos-Renyi random graphs. We rely heavily on martingale convergence techniques, and concentration properties of (super) martingales. This paper is part of a programme initiated in [16] to study the near-critical behavior in inhomogeneous random graphs of so-called rank-1.

引用

页码：1682 / 1703

页数：22

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