Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generating stationary random graphs on $\mathbb{Z}$ with prescribed
  i.i.d.\ degrees   Let $F$ be a probability distribution with support on the non-negative
integers. Two algorithms are described for generating a stationary random
graph, with vertex set $\mathbb{Z}$, so that the degrees of the vertices are
i.i.d.\ random variables with distribution $F$. Focus is on an algorithm where,
initially, a random number of "stubs" with distribution $F$ is attached to each
vertex. Each stub is then randomly assigned a direction, left or right, and the
edge configuration is obtained by pairing stubs pointing to each other, first
exhausting all possible connections between nearest neighbors, then linking
second nearest neighbors, and so on. Under the assumption that $F$ has finite
mean, it is shown that this algorithm leads to a well-defined configuration,
but that the expected length of the shortest edge of a vertex is infinite. It
is also shown that any stationary algorithm for pairing stubs with random,
independent directions gives infinite mean for the total length of the edges of
a given vertex. Connections to the problem of constructing finitary
isomorphisms between Bernoulli shifts are discussed.

1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph