Strict monotonicity of critical points in independent long-range percolation models
Probability
2025-10-31 v1 Mathematical Physics
Combinatorics
math.MP
Abstract
We consider independent long-range percolation models on locally finite vertex-transitive graphs. Using coupling ideas we prove strict monotonicity of the critical points with respect to local perturbations in the connection function, thereby improving upon previous results obtained via the classical essential enhancement method of Aizenman and Grimmett in several ways. In particular, our approach allows us to work under minimal assumptions, namely shift-invariance and summability of the connection function, and it applies to both undirected and directed bond percolation models.
Cite
@article{arxiv.2510.26314,
title = {Strict monotonicity of critical points in independent long-range percolation models},
author = {Stein Andreas Bethuelsen and Christian Mönch},
journal= {arXiv preprint arXiv:2510.26314},
year = {2025}
}