Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Giant component of the soft random geometric graph   Consider a 2-dimensional soft random geometric graph $G(\lambda,s,\phi)$,
obtained by placing a Poisson($\lambda s^2$) number of vertices uniformly at
random in a square of side $s$, with edges placed between each pair $x,y$ of
vertices with probability $\phi(\|x-y\|)$, where $\phi: {\bf R}_+ \to [0,1]$ is
a finite-range connection function. This paper is concerned with the asymptotic
behaviour of the graph $G(\lambda,s,\phi)$ in the large-$s$ limit with
$(\lambda,\phi)$ fixed. We prove that the proportion of vertices in the largest
component converges in probability to the percolation probability for the
corresponding random connection model, which is a random graph defined
similarly for a Poisson process on the whole plane. We do not cover the case
where $\lambda$ equals the critical value $\lambda_c(\phi)$.

18
The categories of this paper are: econ
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga