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Sharpness of the phase transition for Voronoi percolation in $\mathbb R^d$

Presented by: 
Vincent Tassion Université de Genève
Wednesday 13th July 2016 - 13:30 to 14:15
INI Seminar Room 1
Take a Poisson point process on $\mathbb R^d$ and consider its Voronoi tessellation. Colour each cell of the tessellation black with probability $p$ and white with probability $1-p$ independently of each other. This rocess undergoes a phase transition at a critical parameter $p_c(d)$: below $p_c(d)$ all the black connected components are bounded almost surely, and above $p_c$ there is an unbounded black connected component almost surely. In any dimension $d$ larger than 2, we prove that for $p
The talk is based on a joint work with H. Duminil-Copin and A. Raoufi. 

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons