Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic properties of random unlabelled block-weighted graphs   We study the asymptotic shape of random unlabelled graphs subject to certain
subcriticality conditions. The graphs are sampled with probability proportional
to a product of Boltzmann weights assigned to their $2$-connected components.
As their number of vertices tends to infinity, we show that they admit the
Brownian tree as Gromov--Hausdorff--Prokhorov scaling limit, and converge in a
strengthened Benjamini--Schramm sense toward an infinite random graph. We also
consider a family of random graphs that are allowed to be disconnected. Here a
giant connected component emerges and the small fragments converge without any
rescaling towards a finite random limit graph.

35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin