Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stationary random graphs with prescribed iid degrees on a spatial
  Poisson process   Let $[\mathcal{P}]$ be the points of a Poisson process on $\mathbb{R}^d$ and
$F$ a probability distribution with support on the non-negative integers.
Models are formulated for generating translation invariant random graphs with
vertex set $[\mathcal{P}]$ and iid vertex degrees with distribution $F$, and
the length of the edges is analyzed. The main result is that finite mean for
the total edge length per vertex is possible if and only if $F$ has finite
moment of order $(d+1)/d$.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th