Approximate zero-one laws and sharpness of the percolation transition in a class of models including two-dimensional Ising percolation
If \(p\) denotes the critical probability for bond percolation, and \(q\) is the critical probability for the matching lattice of the square lattice, then one has the equality \(p+q=1\). The present paper shows that this relation \(p+q=1\) holds for a large class of weakly dependent two-dimension percolation models, which are endowed with representation in terms of i.i.d. random variables. The key in the proof of this result is a new approximate zero-one law.
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