# The critical probability for random Voronoi percolation in the plane is 1/2

@article{Bollobs2004TheCP,
title={The critical probability for random Voronoi percolation in the plane is 1/2},
author={B{\'e}la Bollob{\'a}s and Oliver Riordan},
journal={Probability Theory and Related Fields},
year={2004},
volume={136},
pages={417-468}
}
• Published 14 October 2004
• Mathematics
• Probability Theory and Related Fields
We study percolation in the following random environment: let Z be a Poisson process of constant intensity on ℝ2, and form the Voronoi tessellation of ℝ2 with respect to Z. Colour each Voronoi cell black with probability p, independently of the other cells. We show that the critical probability is 1/2. More precisely, if p>1/2 then the union of the black cells contains an infinite component with probability 1, while if p<1/2 then the distribution of the size of the component of black cells…
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