Quenched Voronoi percolation

Article Article scientifique Article Quenched Voronoi percolation fre 2016 author Ahlberg Daniel author Griffiths Simon author Morris Robert author Tassion Vincent 827363 889-911 10.1016/j.aim.2015.09.005 0001-8708 http://linkinghub.elsevier.com/retrieve/pii/S0001870815003436 We prove that the probability of crossing a large square in quenched Voronoi percolation converges to 1/2 at criticality, confirming a conjecture of Benjamini, Kalai and Schramm from 1999. The main new tools are a quenched version of the box-crossing property for Voronoi percolation at criticality, and an Efron–Stein type bound on the variance of the probability of the crossing event in terms of the sum of the squares of the influences. As a corollary of the proof, we moreover obtain that the quenched crossing event at criticality is almost surely noise sensitive. Voronoi percolation Noise sensitivity Quenched crossing probabilities Dewey 510 25 Section de mathématiques 11 false Advances in mathematics 286 ae8860d3-2529-4721-97db-4934a3824407 Article (Published version) Public 1-s2.0-S0001870815003436-main.pdf 436639 application/pdf openAccess Faculté des sciences / Section de mathématiques

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Quenched Voronoi percolation	Advances in mathematics			2016	517	822

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Tassion, Vincent