环删除随机游弋收敛于通弦SLE2速率估计

The Rate Estimates of Convergence of Loop-erased Random Walk Excursion to Chordal SLE 2

随机Loewner发展(简称SLE)是由O.Schramm引入的在平面上有共形不变尺度的一元参数族,它可以通过解驱动函数为一维布朗运动的Loewner微分方程而得到。在环删除随机走动趋向于径向SLE2的速率估计的基础上,讨论了环删除随机游弋趋向于通弦SLE2的速率估计,并给出了在局部度量Hausdorff意义下其收敛的概率估计。

The stochastic Loewner evolution(SLE)introuduced by Oded Schramm is a one parameter family of conformally invariant measures on curves in the plane,which can be obtained by solving Loewner’s differential equation with driving parameter being a one-dimensional Brownian motion.In this paper,on the basis of rate of convergence of loop-erased random walk to radial,we discuss the rate estimates of convergence of loop-erased random walk excursion to chordal.Finally,we conclude the probabilistic estimates of convergence in the sense of locally Hausdorff metric.