Open Access
September 2011 On the scaling limits of planar percolation
Oded Schramm, Stanislav Smirnov, Christophe Garban
Ann. Probab. 39(5): 1768-1814 (September 2011). DOI: 10.1214/11-AOP659


We prove Tsirelson’s conjecture that any scaling limit of the critical planar percolation is a black noise. Our theorems apply to a number of percolation models, including site percolation on the triangular grid and any subsequential scaling limit of bond percolation on the square grid. We also suggest a natural construction for the scaling limit of planar percolation, and more generally of any discrete planar model describing connectivity properties.


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Oded Schramm. Stanislav Smirnov. Christophe Garban. "On the scaling limits of planar percolation." Ann. Probab. 39 (5) 1768 - 1814, September 2011.


Published: September 2011
First available in Project Euclid: 18 October 2011

zbMATH: 1231.60116
MathSciNet: MR2884873
Digital Object Identifier: 10.1214/11-AOP659

Primary: 60K35
Secondary: 28C20 , 60G60 , 82B43

Keywords: noise , percolation , Scaling limit

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 5 • September 2011
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