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

Gady Kozma; Shahaf Nitzan

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

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arxiv 2401.12397 v1 pith:RO3OYQQJ submitted 2024-01-22 math.PR

Gady Kozma , Shahaf Nitzan This is my paper · ORCID

classification math.PR

keywords inequalityconjecturepercolationbiggercasesconjecturedcorrelation-likecriticality

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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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