Scaling of components in critical long-range geometric random graphs on the 2-dim torus
We consider random graphs on the set of N2 vertices placed on the discrete 2-dimensional torus. The edges between pairs of vertices are independent, and their probabilities decay with the distance ρ between these vertices as (Nρ)−1. This is a versatile example of an inhomogeneous random graph that is not of rank 1. Here, we study the critical phase: the main result is the weak limit of the size of
