Janson, S and Luczak, Malwina (2007) Asymptotic normality of the k-core in random graphs. LSE-CDAM-2007-40. London school of economics and political science, London, UK.Full text not available from this repository.
We study the k-core of a random (multi)graph on n vertices with a given degree sequence. In our previous paper  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:||Monograph (Report)|
|Additional Information:||© 2007 London school of economics and political science|
|Library of Congress subject classification:||H Social Sciences > H Social Sciences (General)|
|Sets:||Departments > Mathematics
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
|Date Deposited:||10 Jul 2008 09:09|
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