A note on the random constrained-degree percolation model on $\mathbb{L}^2$

Marco Ticse

A note on the random constrained-degree percolation model on $\mathbb{L}^2$

Probability 2026-07-28 v1 Mathematical Physics

Authors: Marco Ticse

Abstract

This note considers a constrained-degree percolation model in a random environment on the square lattice, where each vertex is assigned a random degree constraint, and edges attempt to open at random times. We prove that whenever an infinite open cluster exists, it is almost surely unique, implying the positivity of the connectivity function in the supercritical regime.

Cite

@article{arxiv.2607.25277,
  title  = {A note on the random constrained-degree percolation model on $\mathbb{L}^2$},
  author = {Marco Ticse},
  journal= {arXiv preprint arXiv:2607.25277},
  year   = {2026}
}