A reduction of the $\theta(p_c) = 0$ problem to a conjectured inequality

Gady Kozma; Shahaf Nitzan

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arXiv · 2401.12397

A reduction of the $\theta(p_c) = 0$ problem to a conjectured inequality

Gady Kozma·Shahaf Nitzan

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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.

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Gady Kozma, Shahaf Nitzan. 2024-01-22. A reduction of the $\theta(p_c) = 0$ problem to a conjectured inequality. https://arxiv.org/abs/2401.12397

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