Crossing probabilities for Voronoi percolation

Vincent Tassion

doi:10.1214/15-AOP1052

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Home > Journals > Ann. Probab. > Volume 44 > Issue 5 > Article

September 2016 Crossing probabilities for Voronoi percolation

Vincent Tassion

Ann. Probab. 44(5): 3385-3398 (September 2016). DOI: 10.1214/15-AOP1052

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Abstract

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.

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Vincent Tassion. "Crossing probabilities for Voronoi percolation." Ann. Probab. 44 (5) 3385 - 3398, September 2016. https://doi.org/10.1214/15-AOP1052