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


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.


Received: 1 November 2014; Revised: 1 May 2015; Published: September 2016
First available in Project Euclid: 21 September 2016

zbMATH: 1352.60130
MathSciNet: MR3551200
Digital Object Identifier: 10.1214/15-AOP1052

Primary: 60K35 , 82B43
Secondary: 82B21

Keywords: box-crossing property , Crossing probabilities , Russo–Seymour–Welsh theory , Voronoi percolation

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 5 • September 2016
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