skip to content
 

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

Presented by: 
Vincent Tassion Université de Genève
Date: 
Wednesday 13th July 2016 - 13:30 to 14:15
Venue: 
INI Seminar Room 1
Abstract: 
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 $p<p_c(d)$ the probability that there exists a black path connecting the origin to distance $n$ decays exponentially fast in $n$.

The talk is based on a joint work with H. Duminil-Copin and A. Raoufi. 
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons