论文标题
谐波探索器与SLE4的收敛速率
The rate of convergence of harmonic explorer to SLE4
论文作者
论文摘要
使用离散谐波函数及其相应连续版本之间的差异的估计，我们得出了谐波探索器的Loewner驱动函数的收敛速率，并在实际线上以速度4的速度4。基于这种收敛速率，弦$ \ mbox {sle} _4 $的衍生估计以及对谐波探索器路径的尖端结构模量的估计值，我们获得了和谐探索器路径的明确幂律促进速率，以达到弦质$ \ mbox {sle} _4 $ seprem ins seprem ins seprem ins seprem ins seprem ins soprem in seprem ins seprem ins sepremum ins seprem in sepremum ins seprem in seprem in sepremum inspect。
Using the estimate of the difference between the discrete harmonic function and its corresponding continuous version we derive a rate of convergence of the Loewner driving function for the harmonic explorer to the Brownian motion with speed 4 on the real line. Based on this convergence rate, the derivative estimate for chordal $\mbox{SLE}_4$, and the estimate of tip structure modulus for harmonic explorer paths, we obtain an explicit power-law rate of convergence of the harmonic explorer paths to the trace of chordal $\mbox{SLE}_4$ in the supremum distance.
