English

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.

Keywords

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