Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the dense Preferential Attachment Graph models and their graphon
  induced counterpart   Letting $\mathcal{M}$ denote the space of finite measures on $\mathbb{N}$,
and $\mu_\lambda\in\mathcal{M}$ denote the Poisson distribution with parameter
$\lambda$, the function $W:[0,1]^2\to\mathcal{M}$ given by \[ W(x,y)=\mu_{c\log
x\log y} \] is called the PAG graphon with density $c$. It is known that this
is the limit, in the multigraph homomorphism sense, of the dense Preferential
Attachment Graph (PAG) model with edge density $c$. This graphon can then in
turn be used to generate the so-called W-random graphs in a natural way. The
aim of this paper is to compare the dense PAG model with the W-random graph
model obtained from the corresponding graphon. Motivated by the multigraph
limit theory, we investigate the expected jumble norm distance of the two
models in terms on the number of vertices $n$. We present a coupling for which
the expectation can be bounded from above by $O(\log^2 n\cdot n^{-1/3})$, and
provide a universal lower bound that is coupling independent, but with a worse
exponent.

12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat