Quenched Voronoi percolation
2016 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 286, 889-911 p.Article in journal (Refereed) PublishedText
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.
Voronoi percolation, Noise sensitivity, Quenched crossing probabilities
IdentifiersURN: urn:nbn:se:uu:diva-268755DOI: 10.1016/j.aim.2015.09.005ISI: 000364615300020OAI: oai:DiVA.org:uu-268755DiVA: diva2:882519
FunderSwedish Research Council, 637-2013-7302