@article{52bb5187-ad25-43ba-96c7-28ec5f958bbc,
  abstract     = {{<p>We consider random graphs on the set of N<sup>2</sup> 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)<sup>−1</sup>. 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 the largest connected component rescaled with (N<sup>2</sup>)<sup>−2/3</sup> described by a diffusion process. This completes the proof that in all regimes, the model is within the same universality class as the Erdős-Rényi graph.</p>}},
  author       = {{Goriachkin, Vasilii and Turova, Tatyana}},
  issn         = {{0304-4149}},
  keywords     = {{Critical long-range geometric random graphs; Phase transition}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Stochastic Processes and their Applications}},
  title        = {{Scaling of components in critical long-range geometric random graphs on the 2-dim torus}},
  url          = {{http://dx.doi.org/10.1016/j.spa.2026.104927}},
  doi          = {{10.1016/j.spa.2026.104927}},
  volume       = {{196}},
  year         = {{2026}},
}