偶极SLE_(κ)迹与圆盘相交的概率估计

Estimate of the probability that the dipolar SLE_(κ)trace intersects disks

设0<κ<8,首先导出上半平面H={z:Im z>0}内从1到区间(-∞,-1]的偶极SLE_(κ)迹与圆盘相交的概率表达式;然后,得到带形区域S_(π)={z:0<Im z<π}内从0到上边界Rπ={z:Im z=π}的偶极SLE_(κ)迹与圆盘相交的概率估计.这将上半平面H内通弦SLE_(κ)迹的相应概率估计推广到偶极SLE_(κ)的情形.

For 0<κ<8,an expression of the probability that the trace of dipolar SLE_(κ)in the upper half-plane H={z:Im z>0}from 1 to interval(-∞,-1]intersects a disk is derived.Next,we obtain an estimate of the probability that the trace of dipolar SLE_(κ)in the strip domain Sπ={z:0<Im z<π}from 0 to the upper boundary Rπ={z:Im z=π}intersects a disk is obtained.This generalizes the estimate of corresponding probability for chordal SLE_(κ)in H to the case of dipolar SLE_(κ).