Resource title

Asymptotic normality of the k-core in random graphs

Resource image

image for OpenScout resource :: Asymptotic normality of the k-core in random graphs

Resource description

We study the k-core of a random (multi)graph on n vertices with a given degree sequence. In our previous paper [18] 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 nā†’āˆž. 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).

Resource author

Resource publisher

Resource publish date

Resource language

en

Resource content type

Resource resource URL

http://eprints.lse.ac.uk/6810/

Resource license