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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.
Original language  English 

Pages (fromto)  12221267 
Journal  Electronic Journal of Probability 
Volume  14 
DOIs  
Publication status  Published  3 Jun 2009 
Keywords
 dynamic random graphs
 degree distribution
 maximal degree
 sublinear preferential attachment
 moderate deviation principle
 large deviation principle
 BarabasiAlbert model
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Dive into the research topics of 'Random networks with sublinear preferential attachment: degree evolutions'. Together they form a unique fingerprint.Projects
 1 Finished

INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA
Morters, P.
Engineering and Physical Sciences Research Council
1/09/05 → 31/08/10
Project: Research council