Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic normality of the $k$-core in random graphs   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 ${{n\to \infty}}$. 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 $G(n,m)$.

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The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th