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A CLT for winding angles of the arms for critical planar percolation. (English) Zbl 1286.60098

Summary: Consider critical percolation in two dimensions. Under the condition that there are \(k\) disjoint alternating open and closed arms crossing the annulus \(A(\ell,n)\), we prove a central limit theorem and variance estimates for the winding angles of the arms (as \(n\rightarrow \infty\), \(\ell\) fixed). This result confirms a prediction of V. Beffara and P. Nolin [Ann. Probab. 39, No. 4, 1286–1304 (2011; Zbl 1225.82029)]. Using this theorem, we also get a CLT for the multiple-armed incipient infinite cluster (IIC) measures.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
60F05 Central limit and other weak theorems

Citations:

Zbl 1225.82029
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