Refine search
Actions for selected content:
1 results
Limit theorems for the number of crossings and stress in projections of a random geometric graph
- Part of
-
- Journal:
- Journal of Applied Probability , First View
- Published online by Cambridge University Press:
- 01 October 2025, pp. 1-24
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
We consider the number of edge crossings in a random graph drawing generated by projecting a random geometric graph on some compact convex set
$W\subset \mathbb{R}^d$, 
$d\geq 3$, onto a plane. The positions of these crossings form the support of a point process. We show that if the expected number of crossings converges to a positive but finite value, this point process converges to a Poisson point process in the Kantorovich–Rubinstein distance. We further show a multivariate central limit theorem between the number of crossings and a second variable called the stress that holds when the expected vertex degree in the random geometric graph converges to a positive finite value.
