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Random networks with sublinear preferential attachment: Degree evolutions

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Random networks with sublinear preferential attachment: Degree evolutions
2.	Creator	Author's name, affiliation, country	Steffen Dereich; Technische Universität Berlin
2.	Creator	Author's name, affiliation, country	Peter Mörters; University of Bath
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Barabasi-Albert model; sublinear preferential attachment; dynamic random graphs; maximal degree; degree distribution; large deviation principle; moderate deviation principle
3.	Subject	Subject classification	05C80; 60C05; 90B15
4.	Description	Abstract	We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and then have a closer look at the temporal evolution of the degrees of individual vertices, which we describe in terms of large and moderate deviation principles. Using these results, we expose an interesting phase transition: in cases of strong preference of large degrees, eventually a single vertex emerges forever as vertex of maximal degree, whereas in cases of weak preference, the vertex of maximal degree is changing infinitely often. Loosely speaking, the transition between the two phases occurs in the case when a new edge is attached to an existing vertex with a probability proportional to the root of its current degree.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	DFG; EPSRC
7.	Date	(YYYY-MM-DD)	2009-06-03
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/647
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-647
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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