Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the largest component of a random graph with a subpower-law degree
  sequence in a subcritical phase   A uniformly random graph on $n$ vertices with a fixed degree sequence,
obeying a $\gamma$ subpower law, is studied. It is shown that, for $\gamma>3$,
in a subcritical phase with high probability the largest component size does
not exceed $n^{1/\gamma+\varepsilon_n}$, $\varepsilon_n=O(\ln\ln n/\ln n)$,
$1/\gamma$ being the best power for this random graph. This is similar to the
best possible $n^{1/(\gamma-1)}$ bound for a different model of the random
graph, one with independent vertex degrees, conjectured by Durrett, and proved
recently by Janson.

14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th