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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

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.

Citation

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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

Information

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

Subjects:
Primary: 60K35, 82B43
Secondary: 82B21

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 5 • September 2016
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