EJP Reading Tools

Scaling Limits for Critical Inhomogeneous Random Graphs with Finite Third Moments

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Scaling Limits for Critical Inhomogeneous Random Graphs with Finite Third Moments
2.	Creator	Author's name, affiliation, country	Shankar Bhamidi; University of North Carolina; United States
2.	Creator	Author's name, affiliation, country	Remco van der Hofstad; Eindhoven University of Technology; Netherlands
2.	Creator	Author's name, affiliation, country	Johan S.H. van Leeuwaarden; Eindhoven University of Technology; Netherlands
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	critical random graphs; phase transitions; inhomogeneous networks; Brownian excursions; size-biased ordering; martingale techniques
3.	Subject	Subject classification	60C05;05C80;90B15
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2010-11-02
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/817
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-817
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
15.	Rights	Copyright and permissions	The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free to copy, distribute, display, and perform the work to make derivative works to make commercial use of the work under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.