Sharpness of the phase transition for Voronoi percolation in dimension larger than two
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| Description: |
Tassion, V (Université de Genève)
Wednesday 13th July 2016 - 13:30 to 14:15 |
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| Created: | 2016-07-20 09:45 |
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| Collection: | Theoretical Foundations for Statistical Network Analysis |
| Publisher: | Isaac Newton Institute |
| Copyright: | Tassion, V |
| Language: | eng (English) |
| Abstract: | Take a Poisson point process on Rd 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 pc(d): below pc(d) all the black connected components are bounded almost surely, and above pc there isan unbounded black connected component almost surely. In any dimension d larger than 2, we prove that for
p<pc(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. |
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