A CLT for winding angles of the arms for critical planar percolation
Probability
2013-10-07 v1 Mathematical Physics
math.MP
Abstract
Consider critical percolation in two dimensions. Under the condition that there are k disjoint alternating black and white 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.
Keywords
Cite
@article{arxiv.1310.1244,
title = {A CLT for winding angles of the arms for critical planar percolation},
author = {Chang-Long Yao},
journal= {arXiv preprint arXiv:1310.1244},
year = {2013}
}
Comments
20 pages, 3 figures