Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A scaling limit for the degree distribution in sublinear preferential
  attachment schemes   We consider a general class of preferential attachment schemes evolving by a
reinforcement rule with respect to certain sublinear weights. In these schemes,
which grow a random network, the sequence of degree distributions is an object
of interest which sheds light on the evolving structures. In this article, we
use a fluid limit approach to prove a functional law of large numbers for the
degree structure in this class, starting from a variety of initial conditions.
The method appears robust and applies in particular to `non-tree' evolutions
where cycles may develop in the network. A main part of the argument is to
analyze an infinite system of coupled ODEs, corresponding to a rate formulation
of the law of large numbers limit, in terms of $C_0$-semigroup/dynamical
systems methods. These results also resolve a question in Chung, Handjani and
Jungreis (2003).

16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th