English

Percolation threshold for metric graph loop soup

Probability 2024-01-04 v2

Abstract

In this short note, we show that the critical threshold for the percolation of metric graph loop soup on a large class of transient metric graphs (including quasi-transitive graphs such as Zd\mathbb{Z}^d, d3d\geq 3) is 1/21/2.

Keywords

Cite

@article{arxiv.2304.08225,
  title  = {Percolation threshold for metric graph loop soup},
  author = {Yinshan Chang and Hang Du and Xinyi Li},
  journal= {arXiv preprint arXiv:2304.08225},
  year   = {2024}
}

Comments

10 pages, 1 figure; revised version (incl. title), to appear in Bernoulli

R2 v1 2026-06-28T10:08:16.064Z