Right-passage probabilities of $\emph{\textbf{SLE}}_{\bm {\kappa}}$ and critical percolation
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摘要: 给定上半平面内的一个固定点, 获得通弦~$SLE_{\kappa}(0\leqslant \kappa8)$~迹穿过它右边的概率估计公式. 基于左边界概率的结果, 建立了闭单位圆内临界渗流不包含其内一个固定点的概率估计公式. 最后, 利用探索过程与~$SLE_{6}$~的关系, 得到了起点和终点相同的~$SLE_{6}$~迹与自避型路径有同样的分布.
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关键词:
- 通弦~$SLE_\kappa$ /
- 洛纳方程 /
- 调和测度 /
- 临界渗流
Abstract: This paper derived the probability formula for a chordal $SLE_{\kappa}$ trace across a given point in upper half plane $\mathbb{H}$. And on the basis of the left-passage probability, established the probability formula for a critical percolation in a closed unit circle without a given point. Finally, according to the relationship of exploration process and $SLE_{6}$, got that with the same starting and ending point, the trace of $SLE_{6}$ has the same distribution of self-avoiding walk.-
Key words:
- chrodal $SLE_{\kappa}$ /
- Loewner equation /
- harmonic measure /
- critical percolation
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