We consider an anisotropic bond percolation model on Z 2 , with p = (p h , pv) ∈ [0, 1] 2 , pv > p h , and declare each horizontal (respectively vertical) edge of Z 2 to be open with probability p h (respectively pv), and otherwise closed, independently of all other edges. Let x = (x1, x2) ∈ Z 2 with 0 < x1 < x2, and x ′ = (x2, x1) ∈ Z 2 . It is natural to ask how the two point connectivity function Pp({0 ↔ x}) behaves, and whether anisotropy in percolation probabilities implies the strict inequality Pp({0 ↔ x}) > Pp({0 ↔ x ′ }). In this note we give an affirmative answer in the highly supercritical regime.
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