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Random networks with sublinear preferential attachment : degree evolutions


Reference:

Dereich, S. and Morters, P., 2009. Random networks with sublinear preferential attachment : degree evolutions. Electronic Journal of Probability, 14, pp. 1222-1267.

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Official URL:

http://dx.doi.org/10.1214/EJP.v14-647

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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.

Details

Item Type Articles
CreatorsDereich, S.and Morters, P.
DOI10.1214/EJP.v14-647
Related URLs
URLURL Type
http://www.math.washington.edu/~ejpecp/Publisher
Uncontrolled Keywordsdynamic random graphs, degree distribution, maximal degree, sublinear preferential attachment, moderate deviation principle, large deviation principle, barabasi-albert model
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code14716
Additional InformationID number: Article Number 43

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