We prove that the standard Russo–Seymour–Welsh theory is valid for Voronoi percolation. This implies that at criticality the crossing probabilities for rectangles are bounded by constants depending only on their aspect ratio. This result has many consequences, such as the polynomial decay of the one-arm event at criticality.
"Crossing probabilities for Voronoi percolation." Ann. Probab. 44 (5) 3385 - 3398, September 2016. https://doi.org/10.1214/15-AOP1052