Logarithmic convergence of finite projective planes

Márton Borbényi; Panna Tímea Fekete; Aranka Hrušková; Ander Lamaison

Logarithmic convergence of finite projective planes

Combinatorics 2026-06-27 v1 Probability

Authors: Márton Borbényi , Panna Tímea Fekete , Aranka Hrušková , Ander Lamaison

Abstract

In this paper, we study the so-called log-convergence of graphs defined by Bal\'azs Szegedy (arXiv:1504.00858). We answer his Question 4 affirmatively: the sequence of incidence graphs of projective planes over finite fields log-converges, and the limit coincides with that of a particular random graph model.

Keywords

log-convergence projective planes incidence graphs random graph model graph limits

Cite

@article{arxiv.2606.28890,
  title  = {Logarithmic convergence of finite projective planes},
  author = {Márton Borbényi and Panna Tímea Fekete and Aranka Hrušková and Ander Lamaison},
  journal= {arXiv preprint arXiv:2606.28890},
  year   = {2026}
}

Comments

19 pages, 2 figures