Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On coprime percolation, the visibility graphon, and the local limit of
  the GCD profile   Colour an element of $\mathbb{Z}^d$ white if its coordinates are coprime and
black otherwise. What does this colouring look like when seen from a "uniformly
chosen" point of $\mathbb{Z}^d$? More generally, label every element of
$\mathbb{Z}^d$ by its GCD: what do the labels look like around a "uniform"
point of $\mathbb{Z}^d$? We answer these questions and generalisations of them,
provide results of graphon convergence, as well as a "local/graphon"
convergence. One can also investigate the percolative properties of the
colouring under study.

23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ