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Symptotic normality of the k-core in random graphs

Janson, Svante and Luczak, Malwina J. (2008) Symptotic normality of the k-core in random graphs. The Annals of Applied Probability, 18 (3). pp. 1085-1137. ISSN 1050-5164

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Abstract

We study the k-core of a random (multi)graph on n vertices with a given degree sequence. In our previous paper [Random Structures Algorithms 30 (2007) 50–62] we used properties of empirical distributions of independent random variables to give a simple proof of the fact that the size of the giant k-core obeys a law of large numbers as n→∞. Here we develop the method further and show that the fluctuations around the deterministic limit converge to a Gaussian law above and near the threshold, and to a non-normal law at the threshold. Further, we determine precisely the location of the phase transition window for the emergence of a giant k-core. Hence, we deduce corresponding results for the k-core in G(n, p) and G(n, m).

Item Type: Article
Official URL: http://www.imstat.org/aap/
Additional Information: © 2008 Institute of Mathematical Statistics
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 23 Jan 2009 15:52
URL: http://eprints.lse.ac.uk/22190/

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