Loop percolation versus link percolation in the random loop model
Probability
2025-09-18 v2
Abstract
In [Muhl2019], Peter M\"uhlbacher showed that in the random loop model without loop weights, a loop phase transition (assuming it exists) cannot occur at the same parameter as the percolation phase transition of the occupied edges. In this work, we give a quantitative version of this result, specifying a minimal gap between the percolation phase transition and a possible loop phase transition. A substantial part of our argument also works for weighted loop models.
Keywords
Cite
@article{arxiv.2408.00648,
title = {Loop percolation versus link percolation in the random loop model},
author = {Volker Betz and Andreas Klippel and Mino Nicola Kraft},
journal= {arXiv preprint arXiv:2408.00648},
year = {2025}
}