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Random networks with sublinear preferential attachment: the giant component


Reference:

Dereich, S. and Morters, P., 2013. Random networks with sublinear preferential attachment: the giant component. Annals of Probability, 41 (1), pp. 329-384.

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    Official URL:

    http://dx.doi.org/10.1214/11-AOP697

    Abstract

    We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree. We give a criterion for the existence of a giant component, which is both necessary and sufficient, and which becomes explicit when f is linear. Otherwise it allows the derivation of explicit necessary and sufficient conditions, which are often fairly close. We give an explicit criterion to decide whether the giant component is robust under random removal of edges. We also determine asymptotically the size of the giant component and the empirical distribution of component sizes in terms of the survival probability and size distribution of a multitype branching random walk associated with f.

    Details

    Item Type Articles
    CreatorsDereich, S.and Morters, P.
    DOI10.1214/11-AOP697
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusPublished
    ID Code26621

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