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Quenched Voronoi percolation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden..
Univ Oxford, Dept Stat, Oxford OX1 3TG, England..
IMPA, Rio De Janeiro, RJ, Brazil..
Univ Geneva, Dept Math, Geneva, Switzerland..
2016 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 286, 889-911 p.Article in journal (Refereed) PublishedText
Abstract [en]

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.

Place, publisher, year, edition, pages
2016. Vol. 286, 889-911 p.
Keyword [en]
Voronoi percolation, Noise sensitivity, Quenched crossing probabilities
National Category
URN: urn:nbn:se:uu:diva-268755DOI: 10.1016/j.aim.2015.09.005ISI: 000364615300020OAI: oai:DiVA.org:uu-268755DiVA: diva2:882519
Swedish Research Council, 637-2013-7302
Available from: 2015-12-15 Created: 2015-12-09 Last updated: 2016-02-05Bibliographically approved

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Ahlberg, Daniel
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