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2013 A CLT for winding angles of the arms for critical planar percolation
Changlong Yao
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Electron. J. Probab. 18: 1-20 (2013). DOI: 10.1214/EJP.v18-2285


Consider critical percolation in two dimensions. Under the condition that there are k disjoint alternating open and closed arms crossing the annulus $A(l,n)$, we prove a central limit theorem and variance estimates for the winding angles of the arms (as $n\rightarrow \infty$, $l$ fixed). This result confirms a prediction of Beffara and Nolin (Ann. Probab. 39: 1286-1304, 2011). Using this theorem, we also get a CLT for the multiple-armed incipient infinite cluster (IIC) measures.


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Changlong Yao. "A CLT for winding angles of the arms for critical planar percolation." Electron. J. Probab. 18 1 - 20, 2013.


Accepted: 23 September 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1286.60098
MathSciNet: MR3109624
Digital Object Identifier: 10.1214/EJP.v18-2285

Primary: 60K35;82B43

Keywords: arm events , central limit theorem , Critical percolation , Incipient infinite cluster , martingale , Winding angle

Vol.18 • 2013
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