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SUMMARY:Sharpness of the phase transition for Voronoi percolation in $\\ma
 thbb R^d$ - Vincent Tassion (Université de Genève)
DTSTART:20160713T123000Z
DTEND:20160713T131500Z
UID:TALK66733@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Take a Poisson point process on $\\mathbb R^d$ and consi
 der its Voronoi tessellation. Colour each cell of the tessellation black w
 ith 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)$:&nbsp\;below $p_c(d)$ all the black connected components are bound
 ed almost surely\, and above $p_c$ there is an unbounded black connected c
 omponent 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 $n$. <br> <br> The
  talk is based on a joint work with H. Duminil-Copin and A. Raoufi.&nbsp\;
 </span>
LOCATION:Seminar Room 1\, Newton Institute
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