A reduction of the $\theta(p_c) = 0$ problem to a conjectured inequality
Probability
2024-01-24 v1
Abstract
We conjecture a new correlation-like inequality for percolation probabilities and support our conjecture with numerical evidence and a few special cases which we prove. This inequality, if true, implies that there is no percolation at criticality on the Euclidean lattice, for any dimension bigger than one.
Cite
@article{arxiv.2401.12397,
title = {A reduction of the $\theta(p_c) = 0$ problem to a conjectured inequality},
author = {Gady Kozma and Shahaf Nitzan},
journal= {arXiv preprint arXiv:2401.12397},
year = {2024}
}
Comments
38 pages, 4 figures