Cardy公式的收敛速率
Rate of Convergence for Cardy's Formula
摘要：
本文证明了在逐段解析Jordan域上的三角形格子上的二维临界点渗流中的交叉概率在网格步长内以幂律速率收敛到Cardy-Smirnov公式给出的极限.我们使用这个结果来获得exp（O（sqrt（log log R）R^（-1/3）的新的上界和下界，该上界和下界表示半平面中原点处的簇具有直径R的概率，改进了先前已知的R^（-1/3+o（1））的估计。
英文摘要：
We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to their limit given by the Cardy-Smirnov formula. We use this result to obtain new upper and lower bounds of exp(O(sqrt(log log R))) R^(-1/3) for the probability that the cluster at the origin in the half-plane has diameter R, improving the previously known estimate of R^(-1/3+o(1)).
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