The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$
The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$
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确定性 Loewner 链的能量：通过 SLE$_{0 }$ 进行可逆性和解释
DOI：
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发表时间：
2016
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通讯作者：
Yilin Wang
中科院分区：
文献类型：
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作者：
Yilin Wang
本文研究了确定性弦Loewner链的能量的一些特征，定义为它的驱动函数的Dirichlet能量。特别是，使用的解释，这个能量作为一个大的偏差率函数SLE$_kappa$作为$kappa$趋于0和已知的可逆性SLE$_kappa$曲线为小$kappa$，我们表明，能量的确定性曲线从一个边界点A的一个简单的连通域D到另一个边界点B，是等于它的时间反转的能量，即。从B到A的曲线。
We study some features of the energy of a deterministic chordal Loewner chain, which is defined as the Dirichlet energy of its driving function. In particular, using an interpretation of this energy as a large deviation rate function for SLE$_kappa$ as $kappa$ tends to 0 and the known reversibility of the SLE$_kappa$ curves for small $kappa$, we show that the energy of a deterministic curve from one boundary point A of a simply connected domain D to another boundary point B, is equal to the energy of its time-reversal ie. of the same curve but viewed as going from B to A in D.