Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The connected component of the partial duplication graph   We consider the connected component of the partial duplication model for a
random graph, a model which was introduced by Bhan, Galas and Dewey as a model
for gene expression networks. The most rigorous results are due to Hermann and
Pfaffelhuber, who show a phase transition between a subcritical case where in
the limit almost all vertices are isolated and a supercritical case where the
proportion of the vertices which are connected is bounded away from zero.
  We study the connected component in the subcritical case, and show that, when
the duplication parameter $p<e^{-1}$, the degree distribution of the connected
component has a limit, which we can describe in terms of the stationary
distribution of a certain Markov chain and which follows an approximately power
law tail, with the power law index predicted by Ispolatov, Krapivsky and
Yuryev. Our methods involve analysing the quasi-stationary distribution of a
certain continuous time Markov chain associated with the evolution of the
graph.

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex