Quenched Voronoi percolation
Probability
2015-01-19 v1 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1501.04075,
title = {Quenched Voronoi percolation},
author = {Daniel Ahlberg and Simon Griffiths and Robert Morris and Vincent Tassion},
journal= {arXiv preprint arXiv:1501.04075},
year = {2015}
}
Comments
21 pages, 2 figures