Bibliographic Details
| Title: |
Exponential decay of connection probabilities for subcritical Voronoi percolation in Rd. |
| Authors: |
Duminil-Copin, Hugo1,2, Raoufi, Aran2 raoufi@ihes.fr, Tassion, Vincent3 |
| Source: |
Probability Theory & Related Fields. Feb2019, Vol. 173 Issue 1/2, p479-490. 12p. |
| Subject Terms: |
Exponential decay law, Connection machines, Voronoi polygons, Percolation theory, Existence theorems |
| Abstract: |
We prove that for Voronoi percolation on Rd(d≥2), there exists pc=pc(d)∈(0,1) such thatfor p0 such that Pp[0connected to distancen]≤exp(-cpn),there exists c>0 such that for p>pc,Pp[0connected to infinity]≥c(p-pc). For dimension 2, this result offers a new way of showing that pc(2)=1/2. This paper belongs to a series of papers using the theory of algorithms to prove sharpness of the phase transition; see [10, 11]. [ABSTRACT FROM AUTHOR] |
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| Database: |
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