Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of the vacant set left by random walk on random graphs,
  Wright's constants, and critical random graphs with prescribed degrees   We provide an explicit algorithm for sampling a uniform simple connected
random graph with a given degree sequence. By products of this central result
include:
  (i) continuum scaling limits of uniform simple connected graphs with given
degree sequence and asymptotics for the number of simple connected graphs with
given degree sequence under some regularity conditions, and
  (ii) scaling limits for the metric space structure of the maximal components
in the critical regime of both the configuration model and the uniform simple
random graph model with prescribed degree sequence under finite third moment
assumption on the degree sequence.
  As a substantive application we answer a question raised by Cerny and
Teixeira by obtaining the metric space scaling limit of maximal components in
the vacant set left by random walks on random regular graphs.

7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph