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We prove a general Russo-Seymour-Welsh result valid for any invariant planarpercolation process satisfying positive association. This means that theprobability of crossing a rectangle in the long direction is related by ahomeomorphism to the probability of crossing it in the short direction. Thishomeomorphism is universal in the sense that it depends only on the aspectratio of the rectangle, and is uniform in the scale and the considered model.

Crossing probabilities for planar percolation