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Consider critical percolation in two dimensions. Under the condition thatthere are k disjoint alternating black and white arms crossing the annulusA(l,n), we prove a central limit theorem and variance estimates for the windingangles of the arms (as n\rightarrow \infty, l fixed). This result confirms aprediction of Beffara and Nolin (Ann. Probab. 39: 1286--1304, 2011). Using thistheorem, we also get a CLT for the multiple-armed incipient infinite cluster(IIC) measures.

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