A CLT for winding angles of the arms for critical planar percolation

Changlong Yao (Chinese Academy of Mathematics and Systems Science)

Abstract


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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Pages: 1-20

Publication Date: September 23, 2013

DOI: 10.1214/EJP.v18-2285

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