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给定上半平面内的一个固定点, 获得通弦~$SLE_{\kappa}(0\leqslant \kappa<8)$~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.
Following [3], we consider the boundary WZW model on a half–plane with a cut growing according to the Schramm–Loewner stochastic evolution and the boundary fields inserted
at the tip of the cut and a...
Conformal weldings of random surfaces: SLE and the quantum gravity zipper
Conformal weldings of random surfaces: quantum gravity zipper
2011/2/24
We construct a conformal welding of two Liouville quantum gravity random surfaces and show that the interface between them is a random fractal curve called the Schramm-Loewner evolution (SLE), thereby...
Multi-point Green's functions for SLE and an estimate of Beffara
Multi-point Green's functions for SLE estimate of Beffara
2010/11/22
In this paper we define and prove of the existence of the multi-point Green's function for SLE--a normalized limit of the probability that an SLE_\kappa curve passes near to a pair of marked points i...
Discrete holomorphic parafermions in the Ashkin-Teller model and SLE
Discrete holomorphic parafermions Ashkin-Teller model SLE
2010/12/15
We find discrete holomorphic parafermions of the Ashkin-Teller model on the critical line, by mapping appropriate interfaces of the model to the O(n = 1) model. We give support to the conjecture that ...